The clincher for me is usually how the neck feels when I'm playing it. So, comfort and playability are really important.
Sound-wise, there's so much you can do to change how a bass sounds (on the bass, the amp, pedals etc) - and there are so many external factors that have an impact too (from how everyone else in the band sounds, to how many people in the audience), that it is of secondary importance to me. But I don't do any recording. If you do, you can forget most of this paragraph!
But... I wouldn't buy a bass I didn't like the look of (shape or colour).
Oh, and there's the cost.
And the logo on the headstock (partly for my own benefit and partly when it comes to selling it again).