The Swadians are a powerful faction, with good crossbowmen and cavalry as well as fairly strong infantry.
The differences between the Swadians and Vaegirs are somewhat aesthetic; while each his its own individual strengths (Vaegir Marksmen fire much faster than Swadian Sharpshooters) there are also some weaknesses that balance this out.
Combat strategies
As one of the two original factions, the Swadians have a more developed troop tree than any faction other than the Vaegirs. Swadians boast accurate crossbowmen and durable knights, but the correct use of a varied party is still the key to victory.
Against infantry
If you are using a less developed party, then it's best to keep your ranged infantry in tight with your regulars until ammo is short. Spreading out and charging is the next logical step. High level cavalry should wait behind sharpshooters until enemies begin returning fire. Spread cavalry and charge to avoid the crossfire.
Against cavalry
The Swadians have excellent knights which, when used en masse, have very few weaknesses. Initial charges against cavalry can lose a few men to lances, so it is best to spread out and hang around your ranged units (if you have them)until the enemy breaks their group formation and pursue. Once their advantage is gone, help mop up.
Against archers
Cavalry are the nemisis of archers. Speed is the key, as well as keeping your shield up until you have a shot at an enemy. Spread your knights out and charge early, working your way around the group thinning their numbers until they either fall, or your own foot/ranged men close and finish the job.
Against ranged horsemen
I advise using Crossbowmen with a wall of dismounted man at arms/knights or preferably, footmen/infantry/ sergeants, as your knights will be hard pressed in catching up with a ranged horseman.
Against mixed forces
Against mixed forces? (Most enemy forces) use mixed forces yourself. Although you might like ranged troops providing fire, especially on cavalry, and later infantry, and your horsemen should work on the enemy archers. Ranged horsemen might be very usefull in this case.