I've played too and I think that it's fair to say that Rhodoks suck-ass. I imagined them as the impenetrable wall of death while my crossbow dudes (~10 A7-8 Siegebreakers, about 30 A4 crossbowman) rain hell, but it seems that it's not the case at all. Rhodoks infantry is absolutely garbage, about 40% of their pikemen spawn without a shield, and as you said, their pikes / lances / spears gives them terrible DPS and in close range it wanna makes you puke.
Supposedly specialised in anti-cavalry, I had many times Men-at-Arms or Mameluks tear through my lines like they're not even there, and these bastards most of time pick off my Archers, so I'm forced to close the gap between archers and infantry. It's so underpowered and the loses are so ridiculous that you end up in a perpetual combat state to get money to pay for the dead your battle is gonna cause and whatever you make is going straight into wages.
Anyway, cavalry is absolutely and crazy OP. With 2 units types, I can wipe anything, ANYTHING a lord throws at me even on 3vs1 battle. Dhirim Captain + Men-at-Arms is just ridiculously OP. I always manage to reduce 280 men army with my 100 cavalry into ashes, and that's sometimes with like 3-4 wounded and 0 dead on Normal damage. All I have to do is circle them, use my Men-at-Arms as Cavalry and Dhirim Captains as Custom group that follows my. My Men at arms charge while my Dhirim go around them and charge from behind. Then I force my men at arms to get One-handed weapons (F5 then F5) and it's a slaughter.
Rhodoks needs a serious buff like 100% chance shields and one handers and not just lances because on siege it's a nightmare and on land battles they are useless against cavalry and infantry. Because technically, Swadian cavalry shouldn't tear through Rhodoks infantry lines like they're not even there.
Oh and one last thing, since the recruitement system is greatly different from Vanilla, I'd like to know if Lords are restricted like a player is restricted by money and peasants / mount limits ? Because I've often seen lords with 200+ men getting stackwiped and then come back a week later with 200+ men like nothing happend (looking at you Lord Ryis).
Overall the other kingdoms are fine and well made. Swadian is alright and has it's strength and weakness, Sarranids are perfect, Vaegirs are... well vaegirs (read they suck), Nords are nice, expect the T8 troop a tad bit OP, almost unkillable, other than that it's a great nation, and now Khergits or Ker****s, garbage troops. It's like playing WW2 Japan with their Kamikaze, you launch your Lancers get some first kills and then watch them get raped. Annoying to play and to face but great on campaign map as they are really fast.