When it comes to autocalc battles and kingdom expansion, there's going to be a LOT of randommess. Every Kingdom starts with "claims" to certain lands owned by other Kingdoms, which is the primary motivation for all of the initial wars in the game. However, Kingdoms decide to go to war based on many factors, including their strength, enemy strength, number of ongoing wars, disposition of the monarch, et cetera.
This means in some games, the Nords will clear out Swadia with little effort. In others, Swadia and Vaegir will team up on the Nords and steamroll them. However, when it comes to determining winners and losers, since all kingdoms draw from similar-size recruitment pools initially and all troop strength is equal over a range, it's impossible to say who is going to come out on top at first. So, my point is, don't take just one or two games as indicative of how the AI is doing in its autocalc battles. It really only takes a little push in one direction for a steamroll to happen - say in your case, if the Sarranids were distracted by something else (say another war), it's entirely possible the Khergits began taking city after city without the Sarranids being able to respond, and with every city they captured, they had more territory to recruit from, thus snowballing out faster.
Regarding Khergit sieges: I have noticed the Khergits are very powerful in sieges when the siege map starts you in range of Javelins. However, on maps where the siege starts out further away, and I have a lot of Crossbows at my disposal, they are completely ineffective, because I can kill hundreds of them while taking virtually no losses myself.
I did recall their heavy cav and their archer cav being way too tough a few versions back, and I tried to mellow them out a bit without making them useless.
One tactic you might try that I found very useful: Bring a lot of archers, and then bring a lot of units with large shields. When the siege starts, spread your archers in a line and put the shield-holding units in a line just a tiny bit in front of them, and command them to hold. I've found that the javelins are then mostly caught up on the shields, and meanwhile my archers are thinning the defenders out. Once the javelins and arrows are done flying, I can command my heavy infantry up to fight without losing so many to javelins to the brain.