It should scoop the mids and sound good, sort of like a scooped stingray sound. If it sounds bad, then something is wrong.
It IS totally normal for this dramatic tone change to happen with one pickup all the way up and the other all the way up, or just nearly all the way up. It's like a tiny unevenness in the levels in their volume controls suddenly emphasizes one pickup more than the other in a good way, but if you want them to sum evenly you need to use active pickups (IE: EMG active models) or an active preamp that actually has two buffered inputs before it's own internal pan or double volume controls... like how a mixer works.... which, by the way, is VERY rare. Nearly all bass guitar preamps use a passive pan control (or double volumes) on the pickups and then the pickups go into the single buffered input on the preamp.
The possibility (which a few folks above mentioned) of a pickup being in reverse phase are worth a shot - it's an easy thing to try if you can use a soldering iron to reverse the wires on only one pickup. But if it does NOT fix it, you could actually have had them in phase before and made them out of phase now, in which case, once you do solve the problem (if possible, at least diagnose it), you probably should put it back the way it was, or at least don't forget you reversed one in case you wonder why it sounds weird in teh future.
Another possible problem could be that the pickups are very mismatched. If one has a much higher resistance than the other, it COULD mean that you will hear the higher resistance pickup much more than the other pickup when both are turned on full.... for electrical reasons not worth detailing right now.
So it's worth measuring resistance of each pickup to see what they are. Might need to disconnect a wire from each pickup to do this so they're no longer in the circuit, but I don't have a jazz schematic in front of me right now to tell you if you can get there with volume pot settings and not desoldering a wire.
Also, one pickup could simply be higher output than the other (IE: louder, in which case you'd need to balance them to match well by adjusting pickup heights. I've had to raise a pickup to nearly touching strings and lower the other right into the body of the instrument when they were poorly matched, but doing so can make them blend well, at least.
Those are all things you can try for free, if you're into experimenting with it.
If they're really badly matched pickups it could be worth replacing one with a better match (and sell the one you don't like), or replace both with appropriate set (and sell both old ones).
I mean, maybe it's fine how it is, and you just really hate a scooped sound. Scooped means mids are cut, while lows and highs still come through. I love scooped sound at times, like when slapping... but not always.
