I don't think Bayou Billy is better on Famicom. It's easier, and some stages look slightly different, but that's about it. If you can beat the US version, you'll feel like a champ! Famicom version also lacks the insulting "HA HA HA HA" voice sample!
Castlevania 3 / Akumajou Densetsu is the biggest and most famous example. Famicom version has more advanced music, but enemies do less damage. Also the US version contains minor censoring. Both are great though.