Which one's better? Why?
Whats wrong with the other?

I do both, I switch when playing, I use my thumb pick to do tremelo's and such and I use my fingers for string crossings and such.
What is this, the 25749th time this topic has been discussed? And it always ends the same ugly way.

No one technique is better. There are many brilliant bassist that use their fingers and many brilliant bassists that use a pick. It's purely preferrence.

Each to their own.