There are so many improvements over Heroes of Might and Magic 3, it's crazy how good this game is. From the top of my head:
-spells are available to every hero, so you are no longer screwed because you didn't find earth magic to teleport around;
-speaking of, there is no teleporting around, and consequently no stupid cat and mouse games;
-units have maximum stacking limits, so even if you lose your army you can still catch up instead of facing a gargantuan unbeatable army at the end of a huge map;
-there are no days of the week, and while I did appreciate "It's the week of...", it's more a meme then a meaningful system. Instead, Units grow continuously;
-you can customize your castles with the units you want. You want a mage hero? Then only build units that will fit that role, why not;
-you can convert enemy faction cities to your own faction, instead of being stuck with unit production that you can't even use to the fullest;
-buildings that grant benefits from time to time, like the waterwheels in HoMM3, are sparse, so that the game doesn't feel like a chore simulator where you have to do your mandatory work each monday;
-3 skills to choose from upon leveling up, and they are better suited towards your character;
-no artifact sets, gathering them was simply too cumbersome;
-the AI is good, the UI is great, the art is amazing;
-there is no mana, so you don't need to frantically use for a refresh before big battles;
-last but not least, there is no healing! Prolonging fights just to resurrect all your units, ugh.

In other words, the "one more turn" syndrome is back!