I've never run into a boutique 5 string J that felt so much like a really old instrument. Jimmy's unique low radius 5 string fretboard, use of OLD wood in his build, and his more traditional 'hand made' sort of vibe makes his basses feel totally different from the wonderful, exacting CNC's sort of perfection of, for example, the Sadowsky basses (which I also love for what they are).
The other thing that is really cool is that pickups, preamps, pretty much everything, is OEM, and most stuff is made in the shop. The pickups and preamps are things of wonder to me... just sweet sounding and 'old sounding' to my ear.
So, what you get is a new bass that has at least some of that 'early Fender' feel, look and tone, in an active 5 string instrument, which is pretty remarkable.
In our many, many GTG's in Detroit, the A-C's always really spoke to the J bass guys (I have no experience with Jimmy's P basses at all.... never played one, and I also have little interest in 4 string basses, so can't comment there either).
For those wanting a 5 string J style instrument, and want an active bass with a great B string that sounds more like a passive 4 string, they are quite amazing to me personally.
IMO and many years now of happy IME. Again, not white washing the issues discussed earlier, just answering your question specifically from my experience with my beloved LM (and the LG and RA I owned previously, and the many I have played).