Interesting. There are a lot of things I've liked about 5E--I'll admit I'm not much of an old-schooler, as I started playing with 3.5, switched to 4th Edition for the duration of its support, and started playing 5th edition a few months back.
At first, I really liked what 5th edition did with the game. Combat being quick and decisive is a boon in many cases, and I like there being less fiddly bits to keep track of all the time. Replacing the various small bonuses with advantage/disadvantage is the main thing here, and bounded accuracy keeps things from breaking due to that.
However, the more I play, the more I see some issues. First off is the sheer randomness and unreliability of the system, which is definitely there. Some of this, I imagine, is from the reduction of those "fiddly bits". Putting aside the base math of the system for a moment, in 4th edition, if you were going to be hit by an attack, there were numerous tricks you could utilize to mitigate the hit, if you chose such options when creating your character (you could give them up to hit harder or whatever if you wanted). This is much less true in 5E--such things do exist, but tend to be more costly (a daily spell slot, or an every-4th-level feat).
The gap between the "skilled" and the "unskilled" has grown smaller. No, I'm not talking about power-gamers vs. casuals here, I'm speaking of proficiency. The bonus from proficiency is smaller, and there are less small bonuses you can add to specialize your character in a particular skill. The fact that the number you add to the d20 is now much smaller and you have fewer "fiddly bits" to invest in to make it bigger means that someone who is proficient in a skill is only going to succeed more often than someone else of similar caliber who is not proficient on 3 out of 20 die rolls. This is an issue caused by the bounded accuracy system, and it ties into how "unreliable" things are--it feels as though your choices matter less than the dice. Expertise helps this somewhat, but the fact that it's limited to only two classes and only affects some of their skills is problematic. To use a quick example, the proficiency bonus to a skill at 1st level in 4th edition was +5, and you could easily secure another +2 from race/background/theme choices. To say nothing of certain baseline powers like speak with spirits which could significantly boost skill bonuses. In 5th edition, it starts at +2, and scales up very slowly.
I'll emphasize that I fully understand the benefits of removing all these small bonuses and choices in favor of the much-hailed "bounded accuracy", but I am now coming to terms with the cost and not sure if I like that it was like that. I'd much rather have my cake and eat it too.
5E's swingy, quick combat also is a boon at first that I am starting to see holes in. Notably, and call me a video gamer or whatever if you must, but while I'm cool with the adventurers tearing through a dungeon, having its ups and downs and what-nots, but when they reach the deepest level of the underground lair or the very top of the wizard's tower, there must be a climactic, exciting, cinematic battle to finish things off. And I'm having trouble pulling this off in 5th edition. I want the PCs to confront the evil wizard and have an exciting battle against him and his minions, only for the wizard, upon his death, to transform into a giant scenery-changing old god that warps reality around himself and changes the nature of the fight dynamically.
The problem is, for as flexible as 5th edition claims to be, I find that 5th edition PCs are simply not capable of handling a longer, challenging, dynamic battle (or at least, the majority are not). If the battle is deadly, it must be over quick or the PCs simply will not be able to keep up with the damage/control the enemy is throwing at them. In 4th edition, PCs were durable enough I didn't have to worry as much about this. In 5th edition, I have to be very worried. I'm still trying things here--certainly, one key is having the PCs be fighting the "lair" as much as they fight the "boss", but I'm not entirely certain I want to stick to the lair/legendary action structure--it seems a little rigid to me, and the math constraints of the CR system given in the DMG for balancing monster damage/HP/etc. are rather complex (where are my 5E adventure tools WotC? I used the 4E version of this thing for ages after support for it was discontinued, if just because it handled a lot of the math for me, and 5E did no favors by making the "behind the screen" math even more complicated). I have to question--was this sacrifice necessary? I understand the want for quicker, simpler battles, but did we have to lose the big boss fight in the process? I would hope not, but so far on the DM side it's been a real challenge.
I felt a lot more comfortable homebrewing monsters and encounters in 4th edition than I do in 5th edition. I realize some of this is due to experience with the system, but it seems like the more familiar I get with 5E, the harder it gets, rather than the expected outcome of getting easier. This is because it's really not that flexible, behind the scenes--PCs are flimsier, and they have fewer tricks, so you can't push as hard without breaking them. Monsters also in general tend to be more vulnerable, due to the impact certain spells like Banishment or Wall of Force can have on a fight. Certainly don't plan for monsters to launch team attacks or coordinated assaults outside of surprise situations, because if they're not being OHKO'd by focus-fire or a glass-cannon character, they're being put in encounter-duration time-out by the party caster.
There are also fewer monsters on the board. As CR increases, the amount you can put on the board before the encounter turns "deadly" becomes quite small. 5E combat works best when dealing with small groups of monsters, and starts to show significant problems when it's stretched beyond that. A horde of weak enemies is either trivial if you blast them with a Fireball, or grueling if you're unable to utilize that kind of effect for whatever reason (either you don't have a caster, or the positioning is wrong for it). Very little in the way of "middle ground". Fewer monsters on the board means fewer opportunities for interesting or exciting encounters, unfortunately. Not to say you can't have them, but it certainly limits your options when the system only really works when you do it one way. And the single powerful enemy has most of the problems of older editions, though legendary/lair actions do show that they are learning and getting better at it as a result of how 4th edition solo monsters evolved over the years. I still don't think it's quite there yet though. I wouldn't want to run a solo adult dragon vs. a same-level-as-CR party, as I don't think it would end well for the dragon unless the PCs are incapable of dealing with its ability to fly (which is a pass/fail kind of mechanic that I don't really like).
That turned into a lot more text than intended and I probably rambled at times. Hope I got some points across though, and maybe someone will glean some insight from the struggles I'm having with the transition.
