In the wake of Pedantic's interesting question "
4th Edition - what is it really?" on RPG.net  I decided to collate that thread into a single document with most of  the reasons many of us favour 4e and on which 5e appears to simply not  be delivering at present.  And I'd like some help and advice as to  anything I've missed.
(This is a work in progress with a 
master copy in Gdocs - feel free to comment there)
The design goal of D&D Next is to ensure that anyone can play their  favoured version of D&D in D&D Next.  So far for 4e players  (WoTC’s only current customer base), this appears to be a miserable  failure.  A failure that is not helped by a regular apparent refusal of  the D&D Next development team to acknowledge the way 4th edition  worked starting with Monte Cook’s “Passive Perception” and most recently  with Tom LaPille claiming that the Reaction action is a new thing when  it is exactly the same as the 4e Immediate Reaction action, thus giving  the impression that he either doesn’t know the rules of 4e or doesn’t  care about them.  I’m not sure which would be worse - either indicates  that the D&D Next team doesn’t care about their only current  customer base joining in with D&D Next.  And a significant  proportion of us have game loyalty rather than brand loyalty and so will  not leave 4th to return to earlier, and in our opinion, worse editions  of the game.
So here are a list of things 4e does that are, I believe, integral to  the experience of playing 4e, and that D&D next appears to have  avoided.  I shall tackle each in turn, illustrating how each is a part  of 4E, and then how it fails to materialise in the current drafts of  D&D Next.
-     Balance - Power
-     Balance - Flexibility
-     Clear design and purpose
-     Clarity and Cohesion
-     Teamwork and tactics baked in to the system
-     Options and Variety in play
-     Ease of Play
-     Ease of DMing
-     Monster Design and Tactics
Balance - Power
Power balance is a huge thing in 4e but there are fundamentally two  rules that need to be kept to for a system to be sufficiently balanced.
-     Each class needs to be the best at something
-     What each class is best at should come up regularly and not be made irrelevant
Part 1 means that if we have a class called “fighter” then that class  must be the best at fighting.  It should not be possible to switch them  out for a cleric without anyone noticing much of a difference.  2e and  even post-Unearthed Arcana 1e understood this; fighters gained Weapon  Specialisation making them extremely lethal.  In 4e there are very few  classes (Seeker and Binder) that come to mind that are supernumeraries.   And I don't have to look over the PCs character sheets before setting  the challenges.
Part 2 means that being “best at climbing and jumping” probably isn’t  worth bothering with if the wizard can cast fly (that said, “Wire-fu  master” effectively means the same thing and the 4e Monk is an extremely  nice class).  More to the point, being ‘best at mundane hiding’ is  somewhat pointless if the wizard can cast invisibility and has a vast  array of other spells.
In the D&D Next Playtest we can already see the fighter having  problems with power balance.  The Warpriest with one casting of  Crusader’s Strike and equalising stats, weapons, and themes, hits about  as hard as the fighter.  And is within one Healing Word of the fighter’s  hit points.  This means to put things very simply the Fighter is not  best there is at what he does.  He’s merely a rival for it - and a very  clear design goal for the War Domain was to be as good at fighting as  the fighter.
Balance - Flexibility
Balancing flexibility essentially means that every PC should be able to  contribute something to almost every scene but no PC should be able to  dominate all scenes.  We don’t get the “Decker Problem” from Cyberpunk  2020 where when the Decker/Netrunner is hacking no one else is doing  anything.  This is a massive worry with Vancian casting when the Wizard  can reset his spells from day to day - and hardly a worry at all with  AEDU design.
Fundamentally this is hard to balance with primary spellcasters when you  have different resource allocation rates.  But it seems to barely have  been tried in D&D Next.  When the wizard gains spells he gains  things like Charm Person, and the clerics things like Command and  Silence.  The fighter gains … nothing.  They just gain the ability to  Kill More Stuff.  (The Rogue at least gains night vision which is a good  start).
Clear Design and Purpose
How is everything meant to fit together?  4e is pretty obvious normally  if you have the right kind of mind.  Aspects like roles and power  sources show you clearly what a class is meant to do - that said,  aspects and power sources aren’t the only way to do it.  A one or two  sentence tag and then building everything around that would suffice.   For the 4e Monk it would be “Wire-fu martial arts master.”  For the  fighter it would be “Warrior fast and skilled enough to exploit even the  smallest openings”.
When there’s no central theme but merely a grab bag of abilities, the  class normally fails.  Good examples here are of both the 1e and 3.X  monks, both of which fundamentally did not work as they didn’t know what  they wanted to do (the 3.X monks being especially bad as the multiple  attacks and the fast movement couldn’t work together).  And then there  was the failing by being too strong of the 3.5 Druid.
D&D Next does not appear to have this level of clarity.  Mike Mearls  himself has said they are not sure what to do with the fighter - and  they are working on the idea of a second theme.  The Guardian theme  doesn’t focus on the how at all, to the point that both the Guardian  feats use the same form of action and therefore can not be used  together.
Teamwork and Tactics baked in to the system
In 4e the team is stronger than the group as individuals.  Defenders can  do much more damage if they have allies.  Leaders, especially Warlords,  revolve around teamwork, and controllers are masters of setting people  up for someone else to bash - but can rarely win a fight on their own.   The combat portion of the game is one of teamwork; the only people who  don’t directly both empower and rely on others are strikers.  And the  skill challenge rules when used narratively encourage teamwork in a way  simple skill checks don’t - each member should be working out how to  bring what they are best at to assist in the task.
In D&D Next, there seems to be precisely one ability made  explicitely to assist your allies - the Guardian’s Shield Block.  Also  there is one spell in the preview (Battle Psalm) that buffs the whole  party.  Beyond that, literally every other ability a character has is  ‘selfish’.  Teamwork, especially focus fire, may happen.  But you aren’t  encouraged to play a group of people who can bring more out of each  other than they would bring to the party themselves.  The fighter does  his thing (bashing) as the wizard does his.  And so far there’s no group  skill challenge mechanic to encourage players to work together that  way.
Options and Variety in Play
In 4e every character has a minimum of two at will attacks and one  encounter power - and these can be fairly distinct.  If you don’t want  options you can stay in Poised Assault stance, or play an Elemental  Sorceror whose combat choices are either “I burn him” or “I burn them”.   But if you do, they can be as different as Direct the Strike from Brash  Assault, or Storm Pillar from Freezing Burst.  (For example see this  fight montage using just at will powers).
This is compounded by 4e’s plethora of forced movement powers.  A pit  trap is not just an obstacle, it’s something to throw people in.  A  burning building is not just an obnoxious area to fight, but provides  many ways to maneuver and make things hot for the enemy.  And fighting  on a narrow bridge, you are going to be trying to push each other off as  you attack them.  The environment really matters as something you don’t  just walk around.
In D&D Next, the fighter just hits people.  The rogue just stabs  them (no exploiting Acrobat’s Trick and Acrobatics to show off with  ‘Death From Above’ as in my example).  One cleric mostly bashes enemies,  the other mostly radiant lances them.  Same old, same old.  This is,  quite frankly, tedious after 4th edition - and given the number of  enemies in the Caves of Chaos and the escalated hit points, it’s grindy.
Ease of Play
With the single exception of Rituals, literally everything you need to  play a 4e PC is on the character sheet other than a set list of  conditions.  Other than consulting the various Monster Manuals, I don’t  think my 4e group has looked up a rule in play in the past year.
D&D Next returns to a long spell list, with the spells not on the  character sheet.  This can, of course, be fixed for the PCs with  appropriate software.  But will cause a lot of trouble for the DM with  short statblocks.
Ease of DMing
Most of the time when DMing getting a good answer now is worth much more  than the right answer later.  Out of combat the Skill Challenge DCs  provide an excellent rule of thumb for good DCs to use that will not  break immersion and allow the game to continue without interruption.  In  combat I joke that I need three things to run a fight that’s  interesting in its own right.  1: Interesting monsters, which the later  monsters provide in spades.  2: A narrative hook for the fight (if there  wasn’t one I wouldn’t be running a fight).  3: An interactive terrain  feature or two - which in the case of 4e can be a simple pit or sheer  hill to push monsters and/or PCs over, or a couple of patches of ice on  the ground, or anything really.  
D&D Next doesn’t give me quite such good generic guidelines (this  can easily be fixed).  The monsters are just plain dull so far - with  the idea of giving all the interesting abilities to the ultra-tough  leaders making taking out guards a snooze-fest, and almost every fight  revolve round tactics of either “kill the leader” or “ignore the leader  and defeat in detail” - neither being half as interesting as 4e.   Without regular forced movement I need the interactive terrain to be  active in its own right to be memorable and pivotal - a much harder  proposition.  Which means that the only part of interesting combats from  4e D&D Next hasn’t crippled is the narrative hook for the fight.   The one that isn’t dependent on the rules.
Monster Design and Tactics
Monsters in 4e (at least in the later monster books) are distinctive and  interesting.  Kobolds and goblins, despite being physically quite  similar, behave extremely differently just based on the statblocks.   Goblins are sneaky ambushers who hide lots.  Kobolds are slippery but  often brave bastards who slide past all but the most skilled PCs and who  have craftsmen (tunnellers) who still fight as opposed to all being  brigands.  And to win a 4e fight decisively, the thing to do is to  prevent the monsters playing their game.  It’s to melee the archers, to  prevent the kobolds sliding past you, to keep the battle line at range,  attack the lurkers when they appear, making sure you don’t get flanked  by skirmishers, etc.  A combat in 4e is therefore something to be solved  as much as something to be powered through - with the enemy doing their  combined best to break these solutions and solve the PCs strengths.
Monster statblocks in D&D Next generally appear to be ‘Small sack of  hp’ (kobolds, rats), ‘Medium sack of hp’ (goblins), ‘Big sack of hp  although smaller than a 1st level PC’ (orcs, hobgoblins), ‘Big beefy  grunt’ (ogre), ‘Leader’.  There’s almost no sense of solving the  monsters strengths and making them play to their weaknesses (other than a  ray of frost kite of a big monster).  It’s all about powering through  the enemy - you can’t neutralise the Kobolds advantage except by killing  them, there’s no way to prevent Orcs from charging, or even the Hook  Horror doing its thing. So D&D Next combat is a lot less interactive  and just boils down to “kill them before they kill you” rather than  "outsmart them to kill them more easily".