I prefer flats and choose the lightest guage of whatever brand I buy. I try to play with a light touch and let the amp do the work as much as possible and find the reduced tension helps get the string moving easier.
I have various different different sets on various basses. EB cobalt flats 040-95 on the thunderbirds, thomastik JF344 on the precisions, Fender 9050L 045-100 on the mustangs, status hotwire flats 040-100 on the Guild starfire, The danelectro-specific LaBella 760 FD flats on the longhorn (.042 - 083) and an ancient set of picato double ball flats on the Hohner B2A. I tried a few sets of old strings on my Squier SS jag to see what worked best after I changed the pickups and the ones that came out on top were an ancient set of TI-JF324 that were previously on one of my mustangs.