Pretty compatible
Play-wise, very compatible. I play in a couple games and DM in another, and so far, we have the following:
(TLDR version of the s-blocks below: Through playtests and actual play experience, the Essentials classes intermix well with the classic 4e ones quite well. The play experiences differ (some more than others), and sometimes the essentials ones seem better, but often classic options are missed when the essentials versions are there instead.)
[sblock="FR Game (just made it to level 11):"]
Classic 4e Wizard
Classic 4e Cleric (almost completely unaffected by recent errata)
Hybrid OAssassin|Warlock (looking at revising to Executioner Assassin, now that it is available as a hybrid)
Classic 4e Swordmage
Essential 4e Slayer (brought in to replace an Avenger)
The report from that game is that the Slayer is an upgrade for the Avenger in encounters not involving a lot of difficult positioning and where the Avenger wouldn't use a daily, but in certain situations, we wish we had the Avenger back. (Those Pursuit Avengers get some nice movement abilities, and while their dailies aren't as encounter-changing as the Wizard's can be, they do tend to provide an encounter-long buff of some sort. The Slayer, though, seems to hit harder and just about as accurately.)
The wizard player had a version of the character as a Mage that was tried, but ultimately discarded. That Staff of Defense and (Improved) Tome of Readiness is too nice. When the Wizard was tried as a Mage, it was Pyromancy and Evocation, so more on the damage, but less on the control.[/sblock]
[sblock="Home Brew 'Weird Wars' version of the Civil War (only level 3):"]
Hybrid Artificer|Warlord
--Classic 4e Bard (died early, replaced by above)
Hybrid Rogue|Sorcerer
Hybrid Warlock|Swordmage
--Classic 4e Monk (died alongside the Bard, replaced by above hybrid)
Classic 4e Battlemind
Essential 4e Hunter Ranger (formerly represented by a Seeker)
The play from that game suggests that the Hunter Ranger made a more entertaining controller than the Seeker was, and the concept was either about the same or a slightly better fit. When compared (in my head) to a Wizard, though, neither really measures up as a controller. In this case, the Hunter version does better than the Seeker, but not so much better as to be any kind of an imbalance. The Hunter ranger is a different controller than the Seeker or the Wizard, but then again, the Seeker is pretty different from the Wizard and the Druid, too; they are each different in how they are controllers.
I play the Warlock|Swordmage, and I did builds of him as an Essential Hexblade (and might revisit that with the new Hybrid stuff recently released), and there was really very little difference in many aspects of the versions. I chose the hybrid one so I could tinker more during character advancement, but in game, it seems like there would have been very little difference.[/sblock]
[sblock="Home Brew Classic Fantasy (Just made it to Level 13):"]
This one is an odd example. I DM, and there are no Essentials characters (a Wilden Druid, a Tiefling Paladin, an Eladrin Rogue, a Tiefling Warlock, and a Dragonborn Warlord), but the Eladrin's player tinkered with making the rogue a Thief (dropped the idea because he really likes the Daggermaster PP) and the Paladin has toyed with remaking herself as a Cavalier (she likes her Charisma at-wills and the Hell's Keeper too much to switch, though). The thing that makes it a relevant example is my playtesting of encounters. I tend to use a set of Essential characters in my tests. Here's how I map it.
Druid -- He's a ranged controller and pretty damage-focused, so I use that pyromancer build I mentioned above. In the actual game, I see a lot more proning and dazing, but slightly less damage, than in the playtest.
Paladin -- It's my wife's character, and I helped her build it, so that's what I use.
Rogue -- I use a thief as a stand-in. I think the Daggermaster crits more (though luck prevented a lot of that in the last two or three sessions), but the thief has more consistent damage. It's not by a lot, though. Both are damnably accurate and hit really hard.
Warlock -- I use a Dex-only elf slayer (archery specialized, and I use Power Strike on the bow, even though that's technically against the rules). The damage is a bit less in the game than in my playtests, but the conditions that the Warlock inflicts are sometimes brutal. The player often hit a melee brute with Grasp of the Iron Tower and took it out of the fight (nearly so, anyway) for a round. The other area of difference is when the character gets into melee. The Slayer can switch weapons and hang in there. The Warlock can do a little of that (SK as the two-fold pact allows Hand of Blight), but that player usually gets out of melee -- assisted with Warlock's Wrath -- as quickly as possible.
Warlord -- I use a Warpriest. The Essentials leader pulls off a similar melee presence, but with less interesting leader-y tricks. The Effect lines on the Warpriest's powers do help a bit in making up that slack, though. Really, the leader plays worse in my playtests. Then again, comparing anything to a Warlord in the leader department can be futile, or so I hear.
So of those five characters, I tend to replace four with Essentials-based builds. Granted, the Mage and Warpriest aren't terribly different from Classic 4e builds (having the AEDU structure), but all of the playtests allow me to make predictions pretty well as to the party's performance in actual play. There are some obvious differences, but encounter power levels relative to the parties tends to be similar in the Essentials-based playtests and in the Classic-only actual table experience.[/sblock]
At the risk of sounding defensive (and definitely ninja'd by earlier posters), I've experienced no difficulties meshing characters that are built with mostly Essentials and those built with mostly Classic stuff into the same party. In fact, I don't see it as a situation of having two games, but of one game with a variety of possible character-building options. For rules material, the Rules Compendium is my personal go-to reference. For character building, we use all the options available. For treasure distribution, each DM does their own thing, and none of us use either the parcel system or the rarity system.
It is my experience that Classic 4e characters run fabulously alongside their essentials brethren. There are some differences, to be sure. The Essential defender aura is simpler to run (and, as Aegeri is fond of pointing out, simpler to avoid or nullify) than the marks of a Classic 4e defender, but it does a similar job. What's more, aside from errata that changed powers (which happened a lot before Essentials, too), characters made under Classic 4e remain legal and able to pull of most if not all the same tricks when run next to an otherwise-Essentials party. (The playtest with my wife's paladin and her actual play experiences being so similar is my anecdotal evidence, here.)
I don't think it is just the Essentials release that has prompted the changes to some of the old rules. Wizards of the Coast has been updating the rules since the PHB1 was released (stealth, anyone? or how about the worst-offending Ranger powers?). In some cases, it's about time they got to the issues that are just now being addressed. (Clerics out-controlling Wizards for one; that annoyed me.)
As to telling new players where to start, it's easy for me. It's been a while since I did it (and last time, it was actually a Mutants and Masterminds 2e game), but my philosophy is to start them with a character that matches their preferences. I don't tell people what books to buy; I just help them make a character that can do the sort of thing they want to do in the game. Get them a character sheet that explains their capabilities. If they then want to buy books, I tell them which ones figured prominently in the design of their character. If I had to cold-introduce someone to D&D, I'd recommend a newcomer to gaming start with
one of the HotF* books and an experienced gamer start with
one of the PHB# set (unless they were interested in a specific concept better represented by an Essentials build, like the Hexblade -- then they get the relevant book). Both would benefit from the Rules Compendium, too, for a general overview of all the fiddly bits of playing.
