Having the horrid, broken mess that was the ETW/NTW BAI fresh in memory, the very first thing I did once the game was installed was try a Custom Battle where I gave both the AI and myself an identical 20-unit army each, consisting only of matchlock/musket infantry, a few Light Cavalry and two guns. I picked a flat, open map for ease of testing purposes.
The AI was set to be the attackers, so it was their job to advance on me, while I mostly waited. They advanced in a simple two-line formation, like in regular Shogun 2. Once they had gotten close to me, I told each of my units to attack the enemy unit directly in front of them. There were absolutely no tactics involved on my part; I simply wanted to see how the AI would handle a ranged-only line battle.
The results were... mixed. As both armies came within range of one another, a large portion of their army just kept on walking straight forward as my soldiers were firing away at them. Since reloading time is generally pretty short in FotS, they managed to take a lot of casualties that way. They also tried a cavalry charge at the right wing of my army, but that's where I had stationed my own cavalry as well, so they were intercepted before they could do much damage.
Eventually, all the enemy units finally stopped, and started returning fire. The exchange of fire went on for a few minutes, and here it was a bit hard for me to see what was going on because of all the smoke. Eventually, they were all broken and fled almost simultaneously. The result was a very clear victory on my part, with their army having suffered some 1800+ casualties, and my army only some 700+. I should be noted that I also got a bit of a "head start" in the killing because my cannon started shooting at them and killing them long before they were able to get their own cannon slowly marching into range.
What did I learn of the AI? It definitively seemed improved over ETW and NTW, but still certainly not quite working. I eventually got the musket line-battle I wanted, but it took a while, because the AI was slow to actually stop and shoot back. It also seemed to get a bit confused sometimes. A couple of times, I zoomed the camera close in order to see what was going on in the middle of all the smoke, and I saw a few instances of one unit standing directly in front of another unit, blocking them from firing. I also never really saw the AI using any Abilities; but again, there were lots of smoke everywhere and I mostly stayed on furthest zoom-angle in order to see what the AI army was doing as a whole.