Everyone's got their opinions, but here's my take on them:
Swadia: Theoretically has one of the most powerful troop trees (with exception of the lackluster horse archer, and the bow nerf hits a lot of the archers hard) with heavy cavalry, skilled archers, and surprisingly decent infantry; but they start in position to be potentially attacked by EVERYONE. More often than not, the AI is off campaigning to get back some castle out in the Kherjit boondocks while Praven and Suno burn. It also doesn't help that Uxhal is one of the worst cities to defend.
Of all the games I've played, I've rarely ever seen Swadia rise to prominence without player intervention.
Nords: They usually spread across the map somehow, despite having one of the most lackluster trees out there (not even light cavalry to take out stragglers, and those high level throwers are a joke). I dread sieging their cities, let alone get in throwing range of a Nord army, but I agree with a lot of people here that their tree is the most gimpy.
Rhodoks: Rhodoks are in the ultimate turtling position: Next door to the beleaguered Swadians, and defending against a northern Sarranid attack (who are often tangled with the Kherjits themselves). Their troops are probably the best and most heaviest ground troops out there (though their cavalry is nothing more than the I3-4 pikemen on a horse, and the high-tier twohanders often spawn with one handed weapons and no shield. What?
) that can defend any city with extreme tenacity.
I've almost always seen the Rhodoks creep out from the mountains and slowly start to paint the map green. IMO, this is the strongest faction that often needs to be curbed with player intervention.
Sarranids: Swadia of the desert, but with incredible horse archers, crappy infantry and archers that are built like skirmishers (good or bad, depending on your playstyle). It's hard taking them on their own turf, because the Memluks, Hashams, and Iq'Atars will eat you alive. Sarranids are great for outdoors battles, but sometimes leave a little more to be desired in sieges. I notice that they usually hold their own, but sometimes lose Shariz to the Rhodoks.
Kherjits: One of the factions I usually vote to exterminate in the beginning. Not because of perceived power, but because 90% of the fights involve chasing horse archers for 15 minutes. As mentioned, their cavalry and horse archers are their specialty (though the horse archers are a few pegs down from the Sarranids, because the Kherjit bows and arrows frankly suck) and open field battles are their strength. Their high tier archers are surprisingly good, but the infantry are nothing more than speedbumps that eventually become cavalry.
From my observations, Kherjit map painting is wildly variable: Sometimes they get wiped out fast, sometimes they grow to prominence. Though, in any siege that doesn't favor attacking archers, expect them to get mowed down by the dozen.
Vaegirs: The Vaegirs have some interesting points (blunt infantry, particularly nasty high tier archers), but overall their troop trees comes off as "Captain Generic". Not bad, but nothing particularly exciting. Maybe the lower tiers could get blunt weapons to make their troops more feared/give them a edge?
Usually they end up duking it out with the Nords, Kherjits, or both; then either expand or get swallowed up by their neighbors. Plain Jane.