Woodchuck said:
Actually you CAN'T play more notes on a 6. There the same notes, just in different octaves!
Well, you can play a few more notes on a six. You've got a fourth below and a fourth above what you would have on a four.
To me, it's more a matter of how you play and if you need it. I wouldn't take a six string to a blues gig - I'd just look silly with it. But, when I've got a chops gig (where I might get a couple chances to blow), I like the tonality of the notes on the high C. They sound just enough "not like a bass" to make people notice.
Here's the best reason I've come up with so far, though. I'm not sure I have fully integrated this reason into my 6 playing, but...
Bass players, among just about all musicians, tend to structure lines (melodies, especially solos, etc.) in a chromatic or scalar fashion. This is because when you climb up in pitch, you get to the G string pretty fast, and then all you can do is move up the neck.
With a six, you can move across the board to reach more notes, and if you make it a priority to do so, you can work more intervals and arpeggiated tones (versus scalar passages) into your playing.
Plus, they do look cool. You get a lot more comments from people who say they've "never seen one of those before."