I've played with a pick since I started teaching myself bass 12 years ago.
At the time it was out of necessity because I was just starting, in a ska band and couldn't keep pace with my fingers; and since I had strummed a little guitar before then, I already had the picks and knew how to hold them.
Over the years I've learned how to hold the pick in about 10000000 different ways to get a different tone. Also, playing with a pick forced me to change WHERE I pick to get different sounds. Need that twang? Play near the bridge (Ill even rest my hand on the bridge to get some leverage for one hell of an aggressive attack).
If I wanted something a little rounder/warmer, I could just play up near the neck.
Sure, the same is true for finger-style, but (and the dual wielders can prove me wrong here) I feel like the tonal difference is more noticeable with a pick.
The best part of playing with a pick for me is the ability to dig in hard and get some grit instead of relying on pedals/effects. I'm sure guys who are good with their fingers (HA!) can do the same, however I am not one of them and my finger-style is inconsistent and muddy at best.
I know a lot of people say that picks alienate you from the bass 'feel' but once you've played with one long enough, it's as much part of the bass as the strings. Hold the pick loose, tight, or angle it and you can start to hear and FEEL the difference.
I use Dunlop .88's which are pretty thin for a bass pick (from what Ive seen and heard across the inter-webs).
I've also recently picked up some wooden picks from Clayton and a rubber pick from Planet Waves and the tonal difference in material is quite noticeable.
The rubber pick gives me a tone that is VERY similar to finger, but lacks the volume. It still has that "hollowness", but not nearly as hollow as a hard plastic pick.
The wooden picks are somewhere in between the two and may replace my 88's as my go to pick if they can prove to be durable/cost effective enough.
Both the wooden and the rubber picks are a bit thick compared to the 88's, but they still give that great, quick attack.
Another thing to try if you want to mellow the brightness but still use a pick would be using flatwound or ground-wound strings. I have Hofner V knockoff with flatwounds and it sounds very buttery smooth, especially when you roll the treble down a bit.
Random tid-bit: I still casually play guitar (mostly acoustic) and almost never use a pick. All finger-picking and banjo-claw. Different strokes...