I believe that AI decisions for diplomacy are based purely on relative power (faction, military, industrial, economic, etc.) rather than on actual results in a war. In my current game, the Krynn do have much greater power (850 to my 505) than I do, but have failed to appropriately use it. They rarely form fleets and their transports are often undefended (or defended by only one, rather unbalanced ship); only on one occasion have they taken a world from me (a world they originally settled, which I subsequently retook). Otherwise, their damage to me has been limited to picking off constructors and destroying a few shipyards, which I put a stop to by constructing military fleets to defend the shipyards. In a few turns, my blitzkrieg of the Krynn Consulate will continue and they will be wiped out of my cluster completely.
Military and logistical AI seems to be quite poor as well. I have a slight edge over the Krynn in total production, but most of it is social production; the Krynn have far more military production than I do. What's more, a good chunk of my military production (my most productive out of 4 shipyards) is dedicated to making constructors, while the Krynn have a far greater percentage dedicated to actually producing weaponry. Despite this, they seem unable to appropriately use their fleets for a war effort, fighting more like a guerrilla force than the most powerful empire on the map (ships randomly appearing out of the blue in singles or doubles). Since (IIRC) normal difficulty gives full capability to the AI but no bonuses, it's unfortunate that GCIII was released in such an unfinished state.