I play a bit of both. I use the green Tortex 0.88mm picks.
Pick and fingers give quite a different sound, for fast punk I can't get the attack with fingers but for a lot of stuff I prefer the softer attack of finger playing and find muting easier.
Some people seem to think using a pick on bass is cheating or wrong but I just see it as another tool for a different sound. It was good enough for Lemmy, Chris Squier, Justin Chancellor and Paul McCartney so it's good enough for anyone.