OK... I gonna try to be fair to both of the games (I still prefer AoW, just to keep in mind)
Heroes:
HoMM:
- I always disliked the fact, that The Hero itself can only cast spells, but doesn't figth itself (Really disappointing if you're loosing a battle against just a few lowlevel creatures)
+ The stats of a Hero affect the creatures he leads. (e.g. if a Hero gains moving points, the whole party can move further
+ A lot of different 'upgrades' for a Hero, which are for a big part not related to fighting (Navigation, Diplomaticy etc)
AoW:
- Heroes stats don't affect party, which rends them useless to a big part (Speaking of 'Concealment', 'Swimming' if you're not playing lizards, 'Mountaineering' if not playing dwarfs, High Movement rates etc)
+ The Hero can take part of the fight
+ Lot of different Fighting abilities (Different Strikes, Domination and like, Resistances etc)
- Only a few nonfighting abilities
Parties
HoMM:
- Tend's to get to 'I have more Monsters than you'-Games
+ Also weak Monsters can be used since stacks of them are lot bigger than High level monsters
+/- no upkeep required.... (Is good for you, but tends to Unit-Massing games...)
- Never seen a reason for 'splitting' of units, so usually you have 5 stacks with 5 different monster types
AoW:
+ Quality instead of Quantity counts a lot in AoW
+ Lots of balancing has to be done for Parties (Which Unit do you want to take, slow, fast, Ranged, Melee, Resistance etc)
Races/Diplomaticy
Here, AoW wins for my part, since HoMM doesn't really offer a lot of features (No Relations, No Migrating, No Razing/Looting, No Diplomaticy etc...)
All in all I have to say that HoMM is a lot simpler than AoW. This isn't necessairly a bad thing, but I tend to like games with a bit more strategic gameplay than Unit-Massing....
Walky