I have two J's at the moment, a vintage '73 and a 2003 '75 AVRI. They are quite different, the AVRI is natural/maple/black blocks, and the '73 is classic SB/Rosewood/Tort.
The AVRI is light, maybe 8 1/2 lbs, the '73 is about 9lbs 2oz. They sound very different, the '73 is mellow and deep, but can get honky on the back pickup if you need it. The AVRI is much more what you would expect a Jazz to sound like, and can get very funky on the back pickup. I've not had a MIJ, but I had a MIM Roadworn. It was nice to play and very light, but I did have to change the loom and the pickups. I have an '87 MIJ P bass which is a very well made instrument, but again, changed loom and pickup.
If it were me making the decision for you, and you could only buy one bass, I would be looking for a vintage one but at a reasonable weight.
Good luck!
Rob