I'd say play them all - should not be too hard since there are now Sub $500 Squier VM versions of all of those guitars now for a general idea of what they play like. Dunno about the guy in Tad's Jazzmaster. Have not studied their gear much.
I will say all three of those are very different from each other and very different from a Strat....in general.....
Jazzmaster - 25.5" Scale, wide flat pickups that are succeptable to hum, all of the electronics are on one big sheet of plastic so when things go wrong it's harder to fix them without removing the strings or making a big deal out of it. The overall sound is that of like a Pissed off Telecaster with more bass, with a very piano-like delivery to it and a sudsy, spongey bright treble but a thick low and naturally scooped midrange due to the pickup setup. Uses a dual circuit design same as the Jaguar below but uses a 3-way switch instead of individual on/off for each pickup, and has no high pass filter (strangle) like the Jaguar.
Jaguar - 24" Scale, so lighter string tension, and with the Jaguar/Jazzmaster bridge setup this, for most people (not me) means higher gauge strings. Overall tone is similar to a Jazzmaster but with a much more pronounced midrange for some reason, and the attack sound is waaaay different (more of a Tchak than a "ping" - very Duffy initial delivery of notes). Jaguar's have a ridiculously good ability to imitate a Gibson guitar, amazing considering the little strat-like pickups it has, but they are indeed hotter than your average Strat (6.4K = Strat, Jaguar = >6.8K or higher in the bridge typically). They have their faults but can be easily mitigated with careful placement of adjustments and tiny mods. while the Jaguar has 2 more switches than a Jazzmaster, the idea is pretty much the same - 2 circuits, one neck pickup only and uses rollers on the upper horn, and another where each pickup has it's own switch to turn them on and off, plus a high pass filter known as a "strangle switch" that makes the sound tinnier and twangier, and uses conventional volume/tone knobs.
Mustang - 24" Scale, small bodied, offset Student guitar with a totally different vibrato setup. The vibrato, at best, Is kind of like the best of having a Stoptail and a Tune-O-Matic mixed with the worlds smoothest Kahler vibrato ever created, and it can get down and dirty like a Floyd Rose no problem with proper setup. The Mustang sounds somewhere between a Jaguar and a JAzzmaster, a bit less duffy attack due to the different bridge setup, sounds more like a Stratocaster in the bridge, and a Piezo acoustic in the neck, both pickups together in phase gives that sort of oddball springy thing the Jazzmaster has with more mids, and out-of phase it does that whole Peter green "Clonk/Clomp/Honk" thing with more accented treble and high mids. Each pickup has its own switch that changes the phase of the pickup depending on which isde it's on, leading to some redaundant sounding presets.
