Everything except the 4th installment. Only in the 4th part does the hero participate in the battle himself, and you can kill everyone without an army. This is already a different game; it lacks the spirit of Heroes.
And another point – it's a pity that, having outgrown the template of the "best in the series, the third part," the developers didn't outgrow the template of "we didn't finish it? We'll fix it in the next part." The game has very high potential, which... let's be honest, was ruined by a sloppy implementation. But even with what's there, it's enough for a lot.
The same heroes on the battlefield (now truly Heroes, not cowardly rabbits), and what heroes... Powerful wizards, brave warriors, skilled commanders, elusive rogues, and even high-ranking nobility, who don't amount to much on the battlefield, preferring to act outside of it.
A magic system, borrowed from the well-known collectible card game, and it fits perfectly.
A very important thing for me is the elimination of chain actions. In the third part, this flaw of the game was turned into a real art of professional play, no doubt, but watching a squad of troglodytes, having won in the sands of Bracadia and making their way across the land, now clearing out a dwarven stronghold somewhere in the south... My mind refuses to accept this and play in a similar way.
Of the other changes (simultaneous attacks, movement on the battlefield, castle sieges, combining "creatures/heroes" as you like), I won't dwell, but all of them were reasonable and organic, and if anything prevented the "Game of Dreams" (as Sir Kenegam wrote) from becoming one, it was only the all-consuming crudeness. Perhaps the original fifth Heroes from NWC, developing the established ideas, could have become a "masterpiece for the ages" for me, but... "a stroke of the pen, and another page of history is turned," as is the world of HoMM in my life.