Groudon and Kyogre fight because Gamefreak/Nintendo/Anime Producers want them to fight~
Nah :P Anyway, Groudon represents the land and Kyogre represents the sea - conflicting elements you could say, making them eternal rivals and bla bla bla (one wants to expand land, one wants to expand sea). Also Team Magma/Team Aqua fight, and they each control their respective legends, so obviously the legends are going to fight when under the control of one team.
In regards to how Kyogre does not OHKO. The anime is always wierd like that (like Pikachu OHKOs Geodude. Totally legit). Additionally, if you look at it in a more analytical point of view IF Groudon is slower than Kyogre, Drought will activate instead of Drizzle, and Drought negates the super effectivity of Water Spout - and Groudon can probably survive a STAB Water Spout. In the same token, Groudon is a physical attacker and Kyogre's physical defense isn't so good so yeah :P
Also in the anime didn't Groudon have Pikachu on it's side? :O and Pikachu is completely OP
Anyway the reason Kyogre doesn't get an OHKO on Groudon in the anime is because the Producers want to extend the battle and not make it boring. Pokemon Logic :D