Almost finished the second campaign. I'll just comment on the post above and add some rants of my own !
The changes that are immediately noticeable are the skill selection and the resources. The old skill selection system was very randomized, where you got the option to choose one of four different offered bonuses of their own skill trees. The new system allows the player to choose any skill off of all the trees, excepting for level caps and specialization (Might or Magic). Both hero classes can pick skills off of the other's list, but are limited from selecting the tier 3 skills that become available at level 15. There is also a racial ability that is only usable in battle that scales with hero level. I think that this new system is cohesive and relatively balanced, but is not an improvement over the old, randomized system. The randomness of the old systems really helped each game different as you were often forced to pick skills that you might have otherwise avoided, leading to greater hero variety. In HOMM 6, I often find myself making the same hero again and again. Also, the new system lacks that interplay between different skills in which having a certain combination of them allows a hero to obtain a specialized skill. It was always neat to discover these hybrid skills as you played. That's gone now and I feel that a lot of the sense of wonder and discovery goes with it.
The new skill system sucks. It's a HUGE downturn from H5. In 5 the randomness and the class & city specific skills made sure you'd get very different heroes. Over here, if you have a "might" hero, chances are you'll make the same guy 99% of the time. The only difference between them would be the racial ability which they kept from H5 (thank god).
Now, about "magic" heroes ... If you loved playing a mage class in the previous games and having a bazillion spells in your book and casting them to try new strategies, casting them for fun, or just for the overkill then STAY AWAY FROM THIS GAME !!! The spells are SKILLS now. So instead of learning Logistics or smthing, you'll have to learn Slow if you're a mage. This makes you have a very small selection of spells except for very late in the game, so in most cases you'll just cast the same 2 spells tops every battle.
Speaking of battles ... remember how late in the game when you had a huge army and you attacked some random neutral creature stack and it would flee because it was severely outnumbered & outgunned ? Well NOT ANYMORE. You're going to have to fight almost ALL battles. For some reason, the neutral stack disperses only if you outnumber them 1000 times i guess. On the last map i played i had almost 100 upgraded "level7" creatures and hundreds from each of the other creatures, and i still had to fight almost all battles from the map. The only case when the stacks would actually flee was when i fought 10-20 skeletons or goblins. This is by far the most frustrating thing in the game so far. I hate using the quick combat in Heroes games, but this is a necessity here unless you like to fight the same battles over and over and doing the exact same thing in each of them.
I feel the same way about the reduction in types of resources too. It's taking the game in a new direction, and I'm glad that they tried to move the franchise forward, but I just don't think that the new system is really a step in the right direction. This is just my personal opinion, but I found that a lot of fun came from exploring this lush, detailed high-fantasy world with all sorts of crazy creatures and interesting landscapes. The slimming down of the resources available (gold, wood, ore remain, but the exotic materials are all compressed into 'blood crystals' or something) takes away from the complexity of the world itself. It may be a bit easier to manage one's economy now, but I'm not convinced that even that is a good thing. I mean, the economy is pretty simple as it was, I don't think that it needed to be pared down.
Agreed here, it seems oversimplified in this area. Oh and they tease you with it too. The description for the "Week of Sulphur" : "The people of Ashan have not yet discovered a use for sulphur."
One thing that I did really like was the rearrangement of the creature ranks. That is, in previous versions the troops are ranged in power from tier 1 to tier 7. This new system ranks places them into the categories of 'core,' 'elite,' and 'champion.' Creatures of the same tier all have relatively equal utility. One of the criticism voiced earlier in this thread was that all the games end up being very similar and I think that this helps to break that up. Ultimately, any one faction's army will be comprised of the same make up, with all troop types represented. But in the early game, a player must make decisions as to what creatures, of relatively equal utility, to recruit. I think this was definitely a good move and the designer's part. One thing I would have liked to see was having to choose between different creatures like they did in 4. HOMM 4 is widely considered the black sheep of the family (rightly so), but limiting troop selection like that really did a lot to boost replayability.
The creature system in H6 is not bad i guess, but the system in H4 is horrible and didn't boost replayability at all. You just used the same 4 creatures all the time depending on your playstyle. At least in H6 you use the same 7 creatures all the time!

The only game that got it right was H5 with alternative upgrades for all creatures.
I'll find some more things to rant about later prolly.