For me, the necks are critical. I like the Smith necks, they're chunky and my hand doesn't cramp up as much. However, the action isn't as low as on my other basses though and this is also important as I have a light touch. Maybe I need to get the frets re-dressed or something.
String spacing is important too. I prefer narrow spacing (around 16.5mm at the bridge) but enhancements that let a player customise the set up to their taste have to be a good thing. On one of my other basses I have 'compensated' string spacing where the gaps between the strings stay the same, despite the string getting thinner as they go across the fingerboard. This is a really, really nice bit of design for helping to make the bass feel consistent across the strings. I'd also like a bridge which allows 3d movement of the strings and an adjustable nut like that on Warwick basses.
The other important aspect for me is body width. I'm a big bloke (6'4") although not as big as some, and enough body width allows my forearm to get support when I need it. I accept thats not to everyone's taste but there again Fender Jazz basses are relatively wide and we all know how popular they are.
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