A JP7 in Mystic Dream finish and Majesty 2019 in Dark Roast finish.
I know the Majesty-6 and the JP6, so my opinion is based on these.
I want to understand how the Custom Music Man Preamp works and how could this be a pro over the JP7.
The active preamp buffers the signal before it goes to the amp, it's a bit like giving it a little "push". Unlike active pickups, which do amplify output, the JP preamp only "levels" the signal, so the higher frequencies are not lost when travelling through long cables.
I can talk about two pros: (1) it allows fancy electronic circuits to be added, like the 20dB boost and the piezo (in the JP6, the piezo also has a preamp); and (2) is that the tone doesn't become muffled with long cables, and to my ears there's more high-end in the tone (some people say it's the same, but I do hear).
I also talk 2 cons: (1) is that you need batteries 100% of the time: if the batteries die, the guitar is dead; and (2) is that the electronics are far more complex than an ordinary guitar, and all proprietary, Music Man is the only who truly knows how they work.
I would also love to hear how much difference is between tone, feel, playability, etc.
The most noticeable difference to me is that the Majesty neck is wider than the JP6, and it has a flatter fretboard. This makes the JP6 feel more "Strat", and the Majesty feel more "Ibanez". The Majesty is lighter and more ergonomic, with the body shape reminding me of the Ibanez S series when playing stand. Majesty playability is better, but that's just my opinion, I've seen people who felt it "weird".
People love to talk about Majesty upper fret access, but the JP6 is already pretty good in this aspect, so to me it's a minor thing, although noticeable. The short lower horn of the Majesty can give you a "where's the guitar?" sensation, like the neck is free floating in the air.
To my ears, high gain tones sound better with the JP6: the Crunch Lab + LiquiFire combo on the JP6 is absolutely massive. Clean tones sound better with the Majesty, they're more "sparkly". Piezo sounds about the same on both. However, keep in mind that it's all splitting hairs: the tones in JP6 and Majesty are quite similar, that "John Petrucci" signature tone.
Which one of the two should I buy?
I won't answer this one. Collect opinions and test both, then make the choice. Don't go crazy about it, you can always sell one and buy the other in the future.