I've always found the biggest difference between two otherwise equally-skilled players is speed. The more skilled player moves faster, more efficiently, and overall builds a stronger army for late-game. I'll quote one of my earliest games in Heroes II.
The map was Terra Firma, an XL map. I played Necropolis; one of my friends played Knight. I'm obviously advantaged - I have Necropolis on an XL map, while my friend has an early-game race with no prospects of rushing me. But my friend rushed Rangers, then sent his hero off with just Rangers, Pikemen and Swordsmen. They weren't even upgraded, and he took casualties from neutrals every now and then. In the meantime I was happily building up my castle, waltzing my main hero between the mines and neutrals in my corner of the map. The result: my main hero's army included Bone Dragons and a big army while my friend's still had only those Rangers, Pikemen and Swordsmen. But he had 6 castles to my 1, a much higher-level hero and a game-winning advantage without ever facing me in a game.
Compare that with one of my later games in Heroes V. The map is War of the Worlds, and I had Deleb. Playing Brown, I rushed Green down in the first week, moved on to Blue in the second week, Red in the third. It was very fast speed and led to a decisive advantage. After all, speed is what makes the Iron Maiden strong. Take away her early-game power and late-game she's knocked over by a variety of heroes, yet she's Inferno's best hero.
Battle Awareness is important, of course (I remember another game which I lost because I let my Stronghold opponent cast Mass Haste and decimate my stacks before I could react), but Speed simply provides the greater advantage. You can't be really speedy without good map and AI awareness, but even so. In my humble opinion, if you have the mental courage to try for speed you'll greatly improve your results.
I fully believe speed is the lifeblood of Heroes, and the defining factor between a good and a not-so-good player. You can deduce who's better than who before the two fight the final battle simply by seeing who conducts the expansion phase better. The complete player would have every quality, but I don't think many (if any) of us are complete players
Don't mean to put down those who didn't vote for speed though; this is just my opinion, and I can and have been wrong before.
I'm a hypocrite because I suggested that all life is sacred and should not be wasted without good reason.