There are both, but the NPC ones are largely holding players that are very casual or new. Most of what you read about are probably not corporations though, but alliances. Alliances are groups of player owned corporations that work together. The massive battles are mostly fought between these.

What makes Eve interesting is that all star systems except for those in the very middle of the map are controllable by players, and actually provide value to those holding them. So that's why you have these gigantic, drawn out conflicts and large battles where player blocs with thousands of players each are fighting for territory.