Now I understand.
Human versus human. That's something else entirely—a game of wits, egos, and so on.
Unfortunately, we tried playing 4-player online about 2 times, but it glitched a couple of times and that was it; I didn't try again.
But tournament play is probably insanely interesting and no less time-consuming, since the computer moves slightly faster :).

Even offline Tournaments can be very interesting, especially arena-style ones. When the goal isn't just to kill a dumb computer, but to level up your hero and gather troops by a certain deadline—that's a completely different game than standard maps and Campaigns, where there are no criteria other than points.
You start to value everything: building speed, capturing necessary objects, and most importantly, troop losses. And the most interesting part is that the outcome of the game can ultimately be decided by magic, an army, hero stats, or even the artifacts equipped on the hero!
As for online, it varies. It's interesting to play when the forces are roughly equal.