I used to swear by the good ol' Dunlop Tortex .88mm picks- mainly because Metallica used them, and I was 16.
But after falling under the spell of Danny Gatton, I switched to Fender medium teardrops and my playing style changed overnight.
Nowadays, on the rare occasions I play guitar with a pick, I use Jim Dunlop Jazz III picks- ideally with the Tru-Grip rough surface.
For bass I am predominantly a fingerstyle player, but when I need to play with a pick I use thumbpicks. This enables me to switch from one form of attack to another within seconds. I found a brand of thumbpicks other than Jim Dunlop to try called Pickboy- they're much thinner and snappier than the Dunlop thumbpicks with out being too flimsy to withstand bass strings.