Well, as shown Groudon tends to be more playfully grumpy most of the time, unless someone bothers him. In this case, it was Axia. For memories though, Groudon remembers everything. He's got a good memory for things. However, unless it was an order from Claire or Kyo tried something first he'd probably remain passive. Even if they did start fighting, Groudon would probably stop once Kyo did unless he was seriously pissed off about something.

But Claire would probably be able to reign him in.

Probably.