From what I've seen there's no stat changes between classes, it's all just growths? I'm not sure if caps are affected though.
Edit: Apparently there *are* minimum stats, so a unit that promotes gets their stats raised to that minimum, unsure of how this works for re-classing.
Each weapon type has different strengths and arts that you can use. Also, weapons from the triangle still tend to carry similar properties from previous games -- axes have higher might and lower accuracy, swords end up with higher accuracy, lances are in the middle (generally at least).