I find it funny and kind of ironic when the AI's cowardice ends up biting me in the rear. I'll jump from a world I've taken into the gravity well of an adjacent system, and run into a sizable but ultimately inferior AI fleet. It will decide to run in the direction I just came from, arrive at my lightly defended world (what use would I have for defenses if my main fleet was there and I was pushing forward) then proceed to bomb it into oblivion as my fleet races back to chase them off.
When I show up they'll invariably run, so I try to bring a good number of my ships, but not all of them, because most of the time they will retreat back to where they came from and into their own territory, and not deeper into mine. Usually they'll run deeper into their own territory and past my fleet, but I've seen a couple of those weird games of Phase Jump Ping-Pong, with the AI's fleet arriving back to it's world, bumping into half of my fleet, then running back to my world, running back into the other half, and so on (I watched this happen with a sizable group of Siege Frigates for a few minutes before my fleets whittled them into nothing).
But anyway, I would recommend trying to trap the AI into a ping-pong type situation, preferably between at least one of your worlds. Phase Jump Inhibitors are pretty bad, but they do slow down jumping, and if you can get an AI to jump around between systems with them with you in chase you'll have a considerable advantage. There are certain capital ships from the various factions that with the right special abilities can also slow down or stop ships long enough for you to kill them before they jump.
Also, large groups of carriers can be effective all loaded with bombers when trying to pin an enemy AI fleet. The bombers can cross a gravity well very fast, deal a large amount of damage in a single pass and can dispatch many lesser ships in a single pass before they can make a jump.