The A.I. doesn't know how to skirmish, which is pretty critical to maximizing the Wildling's potential, which will generally beat any T5 shield infantry 1v1. Actually just about every Battanian unit is meant to skirmish
I guess they do alright in defense controlled by A.I. due to the amount they can lob before you crash into them.
A big problem with Battania is their troop trees have been ignored for a while (they got some really crappy helmets). Tier 5 units should definitely have more then 25 Head Armor LOL:
The other larger problem with Battania is their lousy map position, they are just kind of doomed to fail being literally in the middle of everything. Also as Ananda said Fians have poor AutoResolve weight, so Battania ends up losing a lot of battles it would generally win due to how good Fians are though. (Though it seems Crossbowmen have gotten a lot stronger, Vlandian Sharpshooters decimate Fian Champions.)
Basically my revised Battania tree looks like this for now, contemplating giving all infantry units a throwing weapon so you can skirmish reasonably with a big infantry blob, though this gets harder the more units you have present. So I have doubts if it's truly worthwhile. Still working on cavalry, hard to find a happy balance since cavalry battles get lop sided very easily.