Many issues
Pros are pretty much the same. Extended range, chords, greater versatility, tapping would be insane on it, more impressive. I moved on from a 5-stringer to a 6-stringer and I -never- used a 4-string. I always wanted to challenge myself, that's part of the reason. Not that 4-string is easier to play, just that I started out with jazz and I'm sticking to it, and the range and versatility it gives me to play from fusion to funk to jazz to pop has always been right on. As usual your choice of genre that you play is very important.
A lot of issues to deal with with a 6-string when you're talking about starting to use the 6-string to its full strength.
If you're using a 5-string and find your B string virtually redundant, don't even think of a 6-string. If you're already finding trouble slapping on a 4-string or 5-string, nail it on a 4 or 5 before even thinking about a 6. If you're finding problems carrying a 5 or 4 stringer (unless you're like me and bought the ULTRA HEAVY squier special V) don't even think about moving to a 6-string.
If your fingers can't stretch out enough on a 5-string or 4-string to reach the bottom notes with finger per fret without curving your finger the wrong way, 6-string would -destroy- your fingers. If you want to do double thumb technique on a 6-string, you -have- to buy one which has either bigger spacing (means heavier and worse for your left hand) or work very hard on your return. Popping D and G just seems so much harder on a 6-string as well. And personal issue with 6-string (I'm not sure whether anyone else has this) is that uneven tone and volume between your lower strings and higher almost naturally.
And floating thumb technique would actually make six string bass a lot more comfortable but comes the other issue of inaccuracy of string comes into play. And adjustment of fingers on the fretboard and your right hard positioning is really a hassle.
If, and only if, you're willing to get past all these issues, and work on it, would you get the fruit of your labour on a six-string. That's what I'm working on. =)
Still a long way to go to reach Adam Nitti's standard... Lol