it's closer to the original american versions, the various parts are of better quality, etc..
in addition to the cloth-covered wiring, the american jags also have different pickups (i think the ones in the japs are the same as japanese strat pickups), different finish (nitro vs. poly), they're all made out of alder (only sunburst japanese ones are), and higher quality jacks and switches.
the japanese ones are fine guitars, there's nothing wrong with them, and i wouldn't say anyone has a huge problem with them... i don't know of anyone on the forum who actually looks DOWN upon japanese jags. it's just that the american ones are comparitively better, and if faced with the choice, price difference aside, i think most people would go for the american one because it's more like a jag than the japanese ones.
there's no problem here, if you don't want to start an argument and you like your jag then everything's cool. i like my japanese one too, it's my grooviest guitar and i STILL don't feel like getting an american one to replace it or anything. when i try american ones in the shop they have a more solid, less abrasive feel to them, a bit less bright acoustically and a little mellower when plugged in too.
Rick from this forum has a great page that can answer all kinds of Jag questions for you if you ask it nicely: http://www.fenderjaguar.net