So, are you asking if a fender jazz is the right bass for you, or are you looking to upgrade your already owned fender jazz?
I am going to assume that you are thinking of buying a fender jazz. I believe that this is a great bass, and incredibly versatile. I mean, the name jazz really doesn't mean anything, as it is a favorite of everyone from metal to folk.
As far as volume, It really depends on what you are running it through. If you get an active jazz bass, those can up the volume a little bit, but you just need the power from your amp, not your bass.
I play a passive MIM jazz, and I love it. Not only is it less expensive with the same bells and whistles, but I don't need to worry about hurting it when I trounce around and stuff, and yet it is classy enough to take to a combo gig at a swanky restaurant and fit right in.
Go for it dude!
I would also say what kind of amp and bass you currently have. Then your fellow tber's can help make suggestions for you.