On a note not related to faction balance, are high-tier horses supposed to be so expensive? I remember seeing a Stubborn Plated Warhorse of some kind in Lannisport and it cost 30,500 gold. That doesn't seem quite right given the prices of other high-tier gear.
After doing a lot of testing as well, I think I'm seeing where the unbalance with the Westerlands lies, army composition and garrisons. AI army compositions have always been incredibly difficult to work with, and for whatever reason the majority of Westerlands armies consist of around 60-75% medium-tier infantry. Reach armies consist of around 60-80% high-tier cavalry, especially Heavy Knights and Knights. Combined with the fact that Reach armies tend to be larger, they have higher numbers and better troops against fewer numbers and worse troops. Right now I think cavalry are a bit overpowered anyway (fight against Dothraki and you'll see what I mean) and even spear and pike infantry can't fight cav worth a damn, so this may need to be looked at. This army composition is the most likely culprit in my mind, as I've seen dozens upon dozens of Reach armies fit this bill completely. As stated above by myself and others, army numbers also seem off. Most Westerlands lords have sub-90 troops, while most Reach lords have over 100 troops in their armies. King Lannister rides around with 220 men, while Lord Tyrell rides with 330-350.
The Westerlands actually isn't too bad at fighting the Stormlands, as Stormlands lords tend to have army compositions of 60-75% medium-tier infantry as well. In one-on-one battles, Westerlands infantry seem quite good, while their archers and cavalry are poor. As I said though, cavalry all around is overpowered right now, and with the Reach having armies where over half the troops are elite cavalry, they dominate the battlefield against the Westerlands and other foes. That may be how it is in the books, but it is quite frustrating that in general there is no counter to cavalry right now in the game, which may be because attack speed bonuses are too high on horseback. Just flank them yourself and hope you can dismount them before they kill your troops, because your troops are powerless to fight them.
Additionally, Westerlands garrisons are wonky by comparison to the Reach's. Reach cities tend to have 350-450 troops garrisoning them, and castles and forts have 120-230 troops. Westerlands cities tend to have 200-300 troops garrisoning them, and castles and forts have 100-180 troops. There may be some number discrepancies in the reinf_kingdom parties for the Westerlands, as lower garrisons basically leave them at a massive disadvantage to all factions. Reach Pikeman, the standard Reach soldier and most common garrison unit, is also greatly superior to Westerlands Men-at-Arms in combat. Try breaking into a Reach city and fighting your way out. Even with damage on its lowest it's impossible.
Lannisport has become my game's Verdun 3.0. Every other day it's besieged by either 1500 Stormlands troops or 1600 Reach troops, taken, then the Westerlands retakes it, and the cycle repeats indefinitely. However, one thing is constant: the Westerlands is fighting a static, losing war. We can't permanently hold any ground because of low garrisons and small armies.