I don't like modern 6-string basses. Not only do they tend to be ugly, they either have four three-or-more-string courses- which seems pretty pointless to me, since it's application would be extremely limited- or they have six individual strings with the same thickness of a regular four-string, requiring the neck to be like three inches wide and look like a wooden plank with metal rods hovering over it. This makes them extremely unwieldy- your hands would have to be extremely flexible and dexterous to maneuver the fretboard. It just looks plain silly to me.
Now, 6-string basses from the '60s are a different matter altogether. The most famous one is probably the Fender VI, which I came to know about through it's use by John on the
Let It Be album whenever Paul was playing piano. Now, the difference between a vintage 6-string and a modern 6-string is that a vintage one has approximately the same neck width of a normal guitar, but it uses a longer scale length, slightly thicker strings, and is of course tuned an octave below a regular guitar. So there's an obvious advantage to this: there's no need to train your fingers in order to play it if you're already familiar with a guitar neck.
Now, when it comes to guitars, my brother prefers wider necks because he learned to play guitar on a nylon string guitar. In contrast, I learned to play a tiny 1960s Silvertone acoustic, so I prefer thinner necks (although I can handle classical guitars and Gretsch guitars just fine). But there's a limit to how much width my brother's hands can take when playing guitar or bass, so a modern 6-string is out the question. None of them are aesthetically appealing to us anyway...
See, the plan is for my brother to eventually learn and compose some very technical basslines, which of course would include making use of bass' entire range. With an old-school 6-string, that range can be expanded even further, even going as far as using guitar techniques- not to mention the potential for using huge and heavy chords.
Thing is- every recording I've heard of a vintage 6-string is nigh indistinguishable from a regular vintage bass, save for the high notes, of course.