Troops that make a difference.

[Didz]

In particular the General's Bodyguard, and even more so if you're talking about one of those 10 dread Mongol general's bodyguards.

Boyars Son's in a nice compact formation plus [HOLD FORMATION] in a narrow city street take Mongol Heavy cavalry down without too much trouble. I suspect any decent heavy infantry or even armoured spearmen would do the same.

[Slaists]

Catholic peasants! In the vanilla game, if in sufficient numbers, they own everything.

[FactionHeir]

Not really. I tried something in M2TW recently that I used to do in MTW:
1 General's bodyguard vs a stack of 20 peasants in custom game.

In MTW, the general would usually end up dead but in M2TW, I managed to beat the peasants each time with about 3-7 bodyguards including general left out of 17.

[Slaists]

I bet, you did it on a flat map with no ostacles to your cavalry charges ;) Try it on a map with varied terrain.

[FactionHeir]

Yep, grassy plain on VH. But it would be easier on varied terrain as I could just easily get all the peasants down to exhausted by having them walk hills and then charge them even more easily.

[Caliburn]

Polish Nobles are pretty useful for the Polish, being pretty OK in melee and carrying around those handy javelins, and available from almost all the castles. I simply love to take on almost any kind of an European army with these guys, HAs are still a problem.

I must agree with Didz with the merc crossbows, they give a huge advantage especially if the enemy won't try to counterattack when he's defending.

And of course, as dismal pointed out, ANY heavy cavalry makes it dirt easy to wipe the AI off the field, especially with a decent enough spear line and a few missiles to keep the HAs at bay.

If you play all the battles, Italians don't even really need castles, as Cavalry militia/Broken Lancers (at least the Venetians, dunno about the others, still a bit new to the game) and their militia spears combined with pavisare form a decent force. The bells are a bother to move, but not bad and add to the feel of the armies. In sieges, heavy inf doesn't hurt though, and everyone loves the variation castles give (I love those Venetian Archers, even if they never get the chance to flank...). Off topic, I know, but I tend to ramble at times.

Highly teched armies can be problematic to replenish if you move quickly, but this is not as big a problem as it could be in Rome. This would suggest that good quality basic troops make the difference.

[Skott]

For Papal States I'd give the nod to Pavise Crossbow men and Swiss Guards. Combine those two and throw in some artillery and nothing will stop you.

But for the main factions I'd say the mercenary crossbow men and spearmen of Western Europe are a godsend in the early years. They are usually better than starting units.