There's definitely something wrong there if I've understood your description correctly. The bridge pickup should have a noticeably brighter sound, less full and with more highs than the other one. Are you saying that it is acutally the opposite? If so, it sounds like you have a wiring issue or a suspect component. But check the height first as Goober suggests - both pickups should be a similar distance from the strings.
Are you familiar with the sort of difference that you should be hearing? For example, how did it sound before the pickup change? Or, do you have access to another Jazz bass you could try in order for you to hear the sort of difference you should expect?
It sounds like you have some idea of how to solder, so you could try connecting the bridge pickup directly to the jack socket temporarily to see if the problem is the actual pickup or somewhere in the wiring/pots. I'd also check for some other possible issues first, though. Do the pots crackle at all when you turn them? Do the solder joints all look sound, and not "dry"? Are there any obvious connections that look suspect, or possibly a short somewhere (something touching/connected to somewhere it shouldn't be)? Do you have a pic or wiring diagram that you can compare with your bass?
This is a just a process of patient elimination and I think you'll discover where the trouble is without too much difficulty. If they're brand new pickups and one is faulty, then you know what to do, I'm sure. Good luck!
