In this vid, the player never switches characters, but just know it's possible. On the right-hand side you also see this... information flow. Those are extra skill effects that get applied randomly based on a probability related to skill level. I won't get into detail here, but here's a link:
http://shrines.rpgclassics.com/psx/so2/skills.shtml#combat
Xillia here goes a bit further and implements team combos, which would be awesome even without the free move ability.