pickup question

I have two solid body electric tenor guitars, and both have a standard tele neck pickup. One of them is noticeably louder and fatter sounding than the other - and the difference is not due to the distance to the strings (in fact, the louder p/u is further from the strings than the quieter one).

Because I otherwise prefer the guitar with the weaker neck p/u, I've been thinking about switching them. My assumption to this point has been that the louder pickup is just that: louder with a higher output. But could the differences in the guitars account for the difference in sound? I get how the same pickup in different guitars will have a different tone, but can the volume itself be affected? I'd hate to go through the trouble of switching them out only to find they both sound like they did before.

As I mentioned, both are solid body tenors, and both have a 23" scale. Same tuning, same string gauges. Same bridge style.

weaker p/u guitar has: bolt-on neck, larger & heavier body, narrower neck.
louder p/u guitar has: neck-through design, smaller & lighter body, wider neck

Any advice appreciated!

Apparently identical pickups can have different lengths of winding for different resistance measurements. You can measure the resistance of each and the stronger one should have a higher resistance, if I understand it. Another possibility is differing magnet setup---some apparently Telecaster-style pickups have only the pole pieces as magnets while some have a ceramic bar magnet underneath.

Another possibility is accidental de-magnetization, which can occur from proximity to large magnets, especially motors with their oscillating fields. A large speaker magnet might be a risk if brought very near the pickup.

All of which is to say, yes, the pickups could have different output strength. Different body would only have very slight effect on tone, other things being equal.