I still regularly play MTW. Never had a chance at playing Shogun unfortunately.
The BAI is very good in comparison to, say, Empire or Rome. They use terrain effectively, use reserves and will often try to flank you with cavalry. Battles in MTW are always very challenging. The only real drawback, as mentioned before, was the primitive diplomacy. Even then, that makes more sense than the one in Empire where nations declare war on you and then don't attack for instance. That really annoys me. If a nation in MTW declares war on you, they have thought it through and will strike fast.