The PATB-1b seems like a safe bet, especially since you have a second guitar that's a likely home for it, if it doesn't do what you want in the first.
The PATB-1b is higher output than the JB. It's also more dynamic, and responds better to volume and tone control.
It's got more highs, but they aren't all in one peak in the upper midrange like the JB, so it actually is smoother.
The JB has wilder harmonics and varying response in the upper register that makes it exciting for solos. The PATB-1b is smoother and more even... But responds more wildly to pick articulation, so you can get varying response another way, and far more controllably.
It's also tighter and more balanced than the JB. It crunches in a way the JB doesn't have the balance for, yet on the same amp/patch single note lines sing like no other pickup I've used. Usually you get brash crunch or singing leads, not both.
Don't know if you've listened to the Custom 5 or Custom Custom any, but I find I can wander between those tones if I set the volume around 85%. Tone up, more like C5. Tone around 75%, mid-80s EVH comes over to say hi.
The Parallel Axis design is odd, it doesn't behave like you'd expect for the resistance. PATB-1b is 15.7K... but a larger coil, I'm reasonably sure it's 43AWG (coils more full with wire than they'd be with 44, also the resemblances to CC/C5 tones), where a conventional coil would usually be 44AWG at that resistance. But despite being fairly high output, it's incredibly dynamic.
The polepiece design has a lot of advantages. Less string pull, longer sustain, enhanced harmonic response, sweeter treble, and terrific articulation. Transients are a bit less harsh, yet it doesn't lack in attack if you dig in with the pick. Notes bloom, oddly tuby response.
I can get pretty much everything I liked about the JB out of it, plus a ridiculous variety more.
[Note: I'm not knocking the JB in other guitars, I love it in other body woods, and it's more flexible if the wood fills out it's lows and highs a bit, rather than emphasizing it's already awesome mids.]