From: Mosquito Bite, Texas
EE has a lot of other improvements, additions, and changes as well. The advanced economy (the one from COG) has had a face lift and works a little differently, and there are a lot of improvements to strategic play. Overall, it's a much more historical game. For example, hoards of Turks no longer appear on the gates of Paris, and there aren't wandering all over the place cossacks anymore. There are several new scenarios that actually make EE several different games. The map is larger and much more attractive, and there are many more provinces which regularize movement and make the economy function somewhat differently, especially for Austria, Russia, and Turkey. The suppy rules have been enhanced and refined, and as Joram says, the detailed naval engagements are quite good.
The AI is quite a bit better, I think. In COG it was very easy to smash the other guy and walk away. But, with the will to fight rules in HW, the strategic attacker must move quickly and decisively, or he will find himself losing the battle. The feel of HW seems to be more like a Napoleonic battle than in COG, which, as you say, was a series of unrelated piecemeal affairs. I find myself preparing flanking maneuvers, movements to the rear of the enemy, etc., far more than I ever did in COG. Since the ability to capture large numbers of troops in the "rout" phase has been eliminated, the battle results seem much better, too.
It's a significant improvement to COG, especially regarding historical faithfulness. COG is a strategy game set in the period (but could easily have been anywhere, and almost any time, IMO). EE is a Napoleonic era strategy game. (Get the subtle difference?)
You'll find it very familiar, yet much different. It's a great game.