They are compatible in the sense that they are using the same terminology, game stats and resolution mechanics. Things like class, race, ability scores, hit points, AC, fortitude, reflex, will, healing surges, healing surge value, attack rolls, damage rolls, saving throws, skill checks, at-will powers, encounter powers, daily powers, utility powers, feats, keywords, damage types, conditions, push, pull, slide, etc. are the same and/or are resolved in the same way in pre and post Essentials 4E.
They are also compatible in the sense that a pre-Essentials 4E character could adventure alongside an Essentials 4E character of the same level and each would be approximately as effective as the other. There is more scope for variation post-Essentials, since some Essentials builds do not have daily powers, but (IMO) the variation is still kept within acceptable limits.
Some feats have been given a power-up in Essentials, but there is nothing to stop a pre-Essentials character from taking Essentials feats.
In addition, WotC has plans to release a
Class Compendium which would further integrate pre and post Essentials characters as it would feature "rules that allow
D&D Essentials characters to select non-
D&D Essentials powers, and it grants non-
D&D Essentials characters access to class features from
Heroes of the Fallen Lands and
Heroes of the Forgotten Kingdoms".