In regards to character building in 4E, do you prefer Core 4E (Player Handbooks and Power Books) or do you prefer the Essential Lines (Heroes of the Lost Lands, Heroes of the Forgotten Kingdoms, Heroes of Shadow, Elemental Chaos, ect)?
Important note : I DM almost always. That said, to build characters either for myself or for players, I like have them both : for most I much prefer the "core" (AED) structure. It works, it has options, you can play the fantasy you want, etc, etc. For some players, I'm glad I have the "one button" classes from "essentials" (who the F thought that was a good name... ?

)
I know the Essentials classes will keep-up with the others (enough for my groups) and it's good that the "I hit with my axe/blast it with fire" crowd get to have a full class (it's not something I found particularly hard to houserule before, but for some, having it come from a book means something.)
Why do you prefer one over the other?
The "core" offer an optic that all characters grow and learn special skills. The other guy with a sword can't do what I just did only a bit weaker (or not even that.)
The Essentials classes felt like they were already built - they felt, to me, exactly like what I do for players that don't want to engage with the mechanics of character building in 4e. "Here's a set of narrow choices."
What are two things that you thought both Core 4E and Essentials did really well?
"Core"
- martial to "other" parity of impact on play (or at least much better)
- pretty much everything worked - and if you found in play that your last choice didn't, you change it easily w/o messing up anything
"Essentials"
- offer "one button characters" : they were something that was missing from the game for a lot of people
- the side-by-side compatibility with what came before (if you mix them up, you can get some weirdness, but, on the whole, not that much)
What are two things that you thought they could have done better with either of them?
"Core"
- "at will" could probably have been something you can add to an attack that's situational. This would have allowed the "I hit it with my axe!" w/o having to narrow the options. As many have pointed out, as play progressed, most characters would really have
an at-will they used, and another that sort of ... stood there looking awkward.
- the presentation was pretty bad for many... And the "build suggestions" which were almost a full page for only the first level of choices made it seem like a huge "thing" to create a character - as opposed to what could have been one of the most pain-free experiences in character building ever : just try it, it'll most probably work. If you find you don't like it : just change that choice.
"Essentials"
- the NAME! Seriously, that was a bone-headed choice of Deific proportions. I just can't get over it. If you want to kill something, that's the way to go.
Note: they are a few things that could have held that label - the Rules Compendium, the Starter Box... But NOT a new PHB! NOOOOO!!!!! What kind of confusing, messed-up tangle of yarn are you trying to create here? What are people supposed to think about a book that's called PHB that's big as it is, that's OLDER, that contains completely different information that's ... not essential? ... o,O ?? So... do I need it? PHB feels like I should need it. Huh... ??? ... Yeah, ok, never mind, I'll try the Pathfinder box instead.
- the resurgence of "complex caster/simple fighter" wasn't great. Plus there were like 3-4 pages of text for each class that felt like they really "imposed" a character concept. The presentation felt more "this is what this is!" vs. "you can use this class to represent a hero that does this, or this, or this character from TV would probably be this, or this"