Tried two times so far, and either I'm just unlucky, or the computer controlled enemies always get Armageddon spell by default, which they use to effectively wear me down by attrition over time.

Anyone knows, if this is intentional, or if I'd start again, there's a chance they won't get it?

The spells are random, but if I'm not mistaken the randomization happens at the beginning of the level. So if you just reload a save from the beginning of the level, they'll just get the same spells.

If you reload the last save from the previous mission if you have it, the spells should re-randomize when you start the next level.

And this level is very tough. My easiest time was with a barbarian for some reason. One time I got luck with the computer player attacking another computer player because it was blocking its path.

It was long ago, and I can't offer specific advice, I just remember that I never finished off all enemies. Just made a dash at the dragon city at some point.

IIRC Magic Guild spells are random (they definitely are in HoMM2), so I guess it's bad luck.
But they should only use Armageddon if they have Dragons (which are immune), or if desperate.

I guess the desperate part applies then, since the city with the spell in its magic guild was a Knight one.
I made a dash for it in current (second) playthrough, here's hoping I manage to hold it, and kill off all their leftover Armageddon-having heroes (and that they won't get the spell in another city).

I was playing as a barbarian too, and yeah, that worked for me. Initially I tried to beat them all, but at one point shrugged, tossed all my barbarian troops together, and while the computer was wasting time grabbing my undefended barbarian castle, mines etc. (still had two castles with all unit buildings and some army, warlock and that knight one with Armageddon spell in its magic guild, that'd slow the computer players down some more if needed), I went for the dragon city and won.
(Ok, cheated a little using the full map code to find it faster, but whatever - as far as my opinion goes, there's actually no such thing as cheating in single player games anyway, because being the only player, whom would I cheat? Computer doesn't count, at the end of the day it's just a glorified gaming board.)

Seconded. I've never managed to beat this map without just going for the dragon city.

I think I did beat this map but it took me a long time to do, and involved conceding castles and taking them back again, and some hit and run tactics to keep grabbing resources. I think you have to time getting the warlock castle back so that the dragons are available, but you haven't had to spend all the resources building the improvements.

I've just loaded up a saved game and my army consists of 34 dragons, 11 cavalry, 33 pikemen, 122 archers and 12 paladins. That seems to be able to beat anything else, but it takes a long time to work around the map picking off the computer players.

If I was to play it again though I think I'd be going direct for Dragon City!

If I remember correctly, I made a beeline for the Warlock city after initial building. You want to hit it just before they get Dragons.