EASY answer here. Get the J48, only because you play a passive jazz. The J48 is made for such instruments as it prevents excessive loading on passive pickups caused by passive DI's like the JDI. Of course, the JDI can work beautifully with passive basses also, but the results will be greatly affected by the length of your instrument cable combined with the length of the XLR/Snake behind the DI. Even the mighty JDI can be trouble with passive basses with long cable runs to the mixer. Besides, any active bass will work fine with J48.
The J48 does require phantom power to operate, which should never be an issue. If you really want the best of both worlds and want to spend a lot of money, the JDV is excellent as it lets you mimic the loading effect created by a passive DI via a drag control. They're a bit pricey though, and require an external power source. For the price of a JDV, you could pickup a JDI and J48.
I play a Lakland DJ which is a passive jazz bass. I've spent a good amount of time comparing the tone between the J48, JDI and a Radial Bassbone, all of which I own and use. Honestly, the J48 wins every time when I do a direct comparison. While the JDI and J48 are both flat, the JDI is a bit more tame up high with a passive bass due to the pickup loading. Some like that, but again the sound will get more and more muffled until it's muddy and distorted as you push longer cables. With the J48 and your passive jazz, you can roll the tone control back a bit to get some warmth and mimic the tone of the JDI. There really is no better gigging DI than the J48 IMHO.