More data on new conquest:
Sending a 279 cruisers fleet to a nearby home planet - 9.7% capture chance.
I've tried with multiple fleet combinations this time, building a fleet and setting it to attack and then checking the info page for the chances. I always built fleets that used up all the available resources, so they can be somewhat compared. Super- and battleships seem to actually give less of a conquest chance than pure cruiser fleets, plus they'd be a lot slower. From the various combinations I tried, a pure cruisers fleet seems to be the most efficient way to spend your resources on conquest fleets.