I guess i'm the odd duck here.....
I use derlin and plastic banjo picks on my fingers and thumb....so i guess technically i use both at the same time....
I found i liked playing with my fingers, but could never quite get the sound i wanted when playing finger style...a banjo player suggested i try his picks which were Nickel they were a bit too bright so i found plastic and derlin ones...
I also use that weird shaped Dunlop and D'andrea derlin shark fin pick that allows you to get different sounds using the different shaped edges
I echo what everyone else has said here.....to be a better or more well rounded bass player you should learn to use both...
your fingers and a pick
Good Luck!