I'm going with Groudon is more or less unchanging, or slow to change - just like the land. Slow, thoughtful, and generally passive. Until someone does something to annoy or agitate him. Then he tends to get violent and highly territorial. He doesn't like it when others intrude upon his own land, especially those who would bring harm to it since he is essentially the embodiment of the land itself.

Ergo, he and Kyo probably fought because he was agitated that her sea tried to intrude upon his land, even if she had no intention of doing that originally. As for Rayquaza, I think he would probably dislike him to the point of holding a grudge for preventing him from raising the land against Kyogre. He doesn't like it when others interferes in a fight of his.

There, I think that works for Groudon~