Honestly, you're comparing two pretty different styles of instruments. A lof of basses out there can nail Precision and Jazz sounds, but there aren't any guitars out there that really feel and sound just like either of those instruments. They are classics, the golden standards of the bass world, and are beasts totally unto their own. Now, that being said, being able to closely approximate those sounds is all you will ever need, as there's nothing wrong with an instrument that has its own sound elements, and that brings our a slightly different shade of whatever your playing style is. The ultimate answer is of course always "whatever sounds and feels better to you", but given that no standard retail outlets carry Carvin instruments, this is one of the rare cases when that answer just doesn't apply.
From what I've heard (both from opinions and from playing), Carins DO nail Jazz and Precision tones, but more importantly they're great sounding instruments and with all the controls they have, the've gotta be some of the more versatile basses out there, tonally. Fenders seem to polarise people a bit these days, with manypeople swearing by them and many others also swearing at the mention of their name. Carvin's mightn't be a "standard", but considering that they are essentially custom-built instruments (predominantly received new by order only), their value is phenomenal. I'm in Australia, so the prices are different here, but less than two grand for a bass built to custom specs is very impresssive. I'm guessing they can afford to do that because they'd have very minimal retail expenses. Small retail presence means small brand publicity, but hell, it's worth it if you can develop a good reputation just through your customer base. We're talking about bass guitars here anyway, not cars or TVs.
Anyway. I've heard, above anything else, that Carvin necks are just some of the best out there, striking the perfect balance between slimness (read "fast") and ridigity (read "meatyness"), which is great IMO because I'm not a fan of ultra-slim Ibanez-style necks. The body designs aren't my favourite, but they're quite unique which is cool, but the older electronics' sound seems to be debatably laudable, but the new ones seem to be unanimously well-received. So all round they just look like great instruments, with very valid entries in the extended range market, and for the price they're just great. Fender's great, but make no mistake, you're paying a premium (no matter where it's made) for that decal on the headstock, a practice I have no respect for.