Title says it all. Doesn't have to be a gym battle, league battle, or COTD specifically. It can be against whoever you want it to be.
This is subject to change for me, but off the top of my head:
OS= Ash vs. Gary @ Silver Conference
Advanced= Ash vs. Brandon? (Final Round)
D/P = Paul vs. Brandon? (Haven't finished Sinnoh yet, but I liked this battle).
What do you guys think?