1.) The Jag-Stang is likely a little thicker because of the humbucker but I think the jarring effect of the change to out-of-phase makes it a bit hard to do a comparison. The best I ever got was comparing an EMG equipped Jag-Stang (mine) to a 1966 Fender Mustang (also mine). The Mustang was a twangier guitar all around due to that bridge pickup, and drastically lower on output.
Also, Mustangs vary from period to period. The vintage ones were wound less as hot (my Mustang had a 5.9K and a 5.3K pair of pickups in it - bridge and neck respectively), but the modern Mustangs Fender makes are typically around 6.4K and a lot of them have Ceramic magnets behind the poles rather than Alnico 2 - they tend to sound a bit fuller with a little less "airiness" to them, and less of the sponginess vintage Mustangs are known for.
2.) I think the balance between the pickups would change, altering the tone, just slightly. Bridge pickups are typically wound hotter than pickups progressively closer to the neck in matched sets on modern electric guitars. When Fender designed the Jag-Stang originally, they probably wanted something to match the DIMARZIO prototype pickup in the bridge, which was likely around 12-16K since that's what Cobain's preferred pickups were wired around (DiMarzio Super Distortions are around 12K, and Seymour Duncan JB are around 16.4K in the bridge). So they probably used a BRIDGE pickup to compensate for the hot humbucker in the bridge position. Plus they did not need a reverse polarity/reverse wound setup to make them cancel hum with both pickups on in phase since the humbucker took care of that except in the neck which would be no different than a regular Mustang (save for increased output). The neck pickup was probably in the 6-7K range.
With a lower output neck pickup, you'll notice it's less distorted, less as gainy, cleaner, and a bit more sparkly. I quite like the mismatch I have in mine - I have a big mean EMG 81 in the bridge and a EMG SA which is basically an active vintage strat type pickup in the neck, the neck is jangly and has a lot of that Mustang sponginess somehow, but the bridge is extremely hot and very distorted, even clean I have a little bit of overdrive, and it's very warm on that guitar - giving me a wide gamut of sounds from just the Jag-Stang alone since I also put a Pi2 Phase inverter in it - and that goes back to question 1 - with a Pi2 phase inverter, I don't lose volume, but it does get that honkey midrangey clonky sound the Mustang is known for, but it's a bit on the thick side due to the hot bridge and the fact the Pi2 has a preamp in it to go with the preamp in the neck pickup. It kind of sounds like James Young's (JY's) Stratocaster he used in STYX in the 1970's with the Yoshinerator preamp in it, just a big growlier and thicker.