I just played both back to back through the same amp (Carr Mercury) with the same settings at different gain levels. Same strings on both, rosewood bridge on both, and volume and tone pots maxed. It’s not scientific but there were some obvious differences. The guitars sound different but at the same time similar due to the same woods and construction. The anti-hums are much more chimey, brighter and airy in these guitars. They also seem to ring longer and maybe sound a little more complex. At times the bridge pickup can sound thinner than the Franz bridge. The Franz sounds tighter, smoother and a little more round if that makes sense. The neck pickup on the Franz is very mellow, almost jazz like. This may also be because it is much lower than the bridge pickup and the volume is slightly less. I can’t imagine how dark and muted it would have sounded if I did not remove the capacitor the factory installed on the selector switch for the neck pickup! I will probably shim it up a little to see the difference. Under gain the anti-hum goes more into the crunch with an edge and the Franz goes a little more bluesy and smooth.
The interesting thing is that I then switched to a different amp (1960 Gibson GA-5T) and the Anti-hums sounded more fat and not brittle at all. The sound seemed to blossom and was very complex sounding. The Franz sounded a little dark and not as interesting to my ears through that amp. However, it had that perfect old school jazz sound when played clean.
I can’t pick one over the other as they are very different sounding. It all depends upon what sound you prefer. I am currently leaning towards the Franz when paired with the Carr amp and the Anti-hum when paired with the Gibson amp. However, I have only had two days playing the one with Franz pickups. Ask me in six month when the new factor has worn off and I have had more time with both