Bass players usually fall into two main categories, some play using just the fingers to pluck the bass strings, whilst others are dyed in the wool plectrum users. There's probably also a third group that is equally happy using both methods and swap around depending on what the song style calls for.
When playing with the fingers it's generally agreed that this creates a much deeper bass sound with less top end due to the softness of the skin plucking the metallic strings, the fingers can also act as a damper controlling the length of sustain when a string is plucked.
By contrast, using a bass plectrum will present a much harder, percussive sound with much more high end frequencies. Bass plectrums are generally much thicker, harder and larger than guitar plectrums although this can vary depending on the individual's choice and their style of playing.