Well... both? At the same time? Unlike 3.0 and 3.5, they really are completely interchangeable. An Essentials "Slayer" can work directly alongside a vanilla 4.0 Warlord.

The only rules differences (there are a few) are errata, corrected in the original rulebooks, and mostly were errata'd before Essentials was published.

In general, I find that some players prefer the more complex AEDU (At-Will, Encounter, Daily, Utility) type classes that are found throughout the earlier products, and some folks prefer to not have as many choices during character creation / leveling / play. Essentials really provides a simpler to work with version of several of the classes. And some of the just before Essentials products use a slightly different mechanic set -- I'm mostly thinking about the Monk and other psionic classes here.

But at the table, I am using the Essentials Rules Compendium. My players are a mix. I'm encouraging them to feel free to take any feat that is in the Essentials books, but check with me before taking older ones, as some of the older ones have versions that are legal but are underpowered, and if you don't know what to look for you might make a choice that would annoy you later.

I'm mostly using monsters from the Essentials Monster Vault, Monster Vault 2 and the old Monster Manual 3. Original MM and MM2 monsters are very useable, but tend to be a bit slower in play and less threatening, so combat goes a bit faster if the later sets are used or the older ones are updated with the MM3 guidelines.

But, in general, I grab monsters, I grab magic items, I allow my players to pick any published 4th edition race or class from any of the sourcebooks, I'm OK with any feat. Essentials is the same ruleset with better layout and presentation.
 

Gurps. 4e
 

Vanilla. Though the essentials classes seem more powerful.
 

The essentials classes are more powerful so I don't think mixing them is a particularly good idea. My group tried using both and we eventually decided to ban essentials characters and go with regular 4E. If you have some new players who aren't hardcore gamers though Essentials is a totally reasonable way to introduce them to the game and has far quicker and simpler character generation. A pity they didn't get the numbers right - in particular the slayer's melee basic attacks are far too powerful in combination with many other character's 'grant a melee basic' abilities.
 

I don't think I agree that the essentials classes are more powerful than "vanilla" classes can be. I do think that "vanilla" classes have a large number of choices, and many of those choices are flavorful but underpowered, or can synergize poorly. But they can also be built in a highly optimized fashion. Essentials classes have few choices, and no choices that lead to weak builds.

Essentials classes only come optimized, to put it another way.
 

Vanilla for the simple reason players are using an old version of the Character Builder without Essentials.
 

This is a must read, comments are great too:

http://community.wizards.com/dndnext/blog/2012/04/06/beyond_class_and_race?pg=1

For 5th they intend to have both styles: Original 4th and Essentials.
 

A solution would be to have a simplified easier character creation (Essential style but alot more choice in the first player handbook instead of rules).

Then first levels gained could give less choices as the PC earns staple class features until let's say 5th level and then let the player have more choices after that level.
 

No, I'm not a paid shill. That said, if you ever follow any advice I give you, follow this: check out the Pathfinder RPG at paizo dot com. Specifically, the Kingmaker adventure path. It's wide open and sandboxy with plenty of room to throw in your own modifications. Plus, it's based on an evolved 3.5 ruleset that actually encourages more "role" and less "roll".

If it does look like something you might be interested in, be aware that the amazon prices are far better than the official website.
 

My group is playing Pathfinder now (the in-all-but-name successor to the 3.5 rules), but our 4E campaign that ended last year was a decided mix of Essentials and straight up 4E. Most of my players prefer the traditional 4E classes, but as DM I found the Essentials build useful for quick NPC generation.