Battle tower:The battle tower doesn't really have anything special.Its just simple battling.There are single battles that allow 3 pokemon,double battles with 4 pokemon,multi battles that allow 2 trainers with 2 pokemon.
Battle hall:In the battle hall you can choose the opponet's pokemon type.It allows 1 pokemon lv30 or up or 2 pokemon that are the same.
Battle castle:In the battle castle it allows 3 pokemon.Your pokemon dont get healed automaticly.You have to use castle points to heal them,restore pp,check opponet's pokemon,level up opponets pokemon(to earn more castle points)or level them down.You can also rent items with castle points.You earn more castle points on how well you did.
Battle factory:Its simple battling but with rental pokemon.You also chose if the pokemon will be lv50 or lv100.It uses up to 3 pokemon.
Battle arcade:The battle arcade uses up to 3 pokemon.Before every battle there is a board that shows up.Press a button to determine a battle's affect.Some of the affects are poison,renting a berry,a sandstorm,hail,and many others.
I hope this guide for the battle frontier will help.