I have both a MIM Jazz and an Epi EB-3 and I'd definately recommend the Jazz. It is good for any kind of music, and more comfortable to play. There is a large selection of pickup and hardware upgrades available. I've played blues, rock and country on mine and it always sounds great.
The EB-3 has a nice neck, but the neck dive is terrible. It only really has one sound, the 3 point bridge sucks, and it is pretty much impossible to slap due to the neck pickup being in the way. There is only one company that makes a pickup that fits, and that is only for the neck pickup. I've also found that it is hard to get a good sound from some amps. It takes a lot of tweaking to sound good. It is good to have for certain situations, but not as a main bass (and I just bought an Epi Allen Woody that is better in those situations anyway). It does look good, and looks are important, but not as important as the other things. Don't ever buy a bass solely because you like the looks.