Hmmm. Well, when they're both starship captains exploring the galaxy, about the same age as each other - I certainly don't want Admiral Kirk meeting Captain Kirk.
If you want a more specific scenario... set it after some specific incident in canon, where both Kirks have just explored the same planet in their respective universes. Preferably an emotionally disturbing incident. And the two Kirks had reacted differently.
I'm sorry, I can't think of a specific canon episode for this, it's too long since I've watched TOS canon.