You're presenting a pretty reasonable question here. And you definitely have a couple of great basses that are a good benchmark of quality. Your instincts from your test drive of the two instruments are likely to serve you well.
I've got a roadworn 60's Jazz bass, and I simply love playing mine. All of the relicing aside, it plays really well and it sounds great. I know there are a lot of people who don't like the concept of a relic'd instrument. If they were to play a roadworn blindfolded, and only had the sound and playability to go by, I suspect their impressions might be far different.
All of that aside, I know how my roadworn plays, and it's great for gigging. I've also been looking for a second Jazz bass over the past several months, because I'd like to have a second solidbody 4-string that I can keep strung with flatwounds. One of the instruments that came to mind was an American Standard Jazz. As much as I love my roadworn, I wanted to go for a different finish. Notably, a black body (tort guard) with a rosewood board. My options along those lines are a little limited, and I wanted to keep my budget for this instrument manageable.
So, I checked out an American Standard Jazz bass. I had one from the 90's, but the tone left me....uninspired. Would this new version, circa 2011, change my opinion? When I tried it out, it was okay. Good enough craftsmanship, solid neck joint, clean fretwork. But tonally? It didn't really compare with my roadworn. And now, my roadworn Jazz is my own benchmark for a good sounding Jazz bass. I really suspect that the difference is because of a few things.
First, the wood for the roadworn instruments seems to be of a select grade. AND, it seems to be kiln dried which seems to help the resonance of the wood. Then there's the finish. The poly finish of the American Standard is pretty good for preserving the instrument. But I really do suspect that it chokes the tone a bit. Whereas the nitro finish of the roadworn instruments allows the wood to breathe more. It's that difference in finishes that generally distinguishes vintage instruments from modern ones. And it should definitely be noted that your American Vintage Jazz bass has the nitro finish.
If you can try out the roadworn Jazz alongside your American Vintage Jazz, I think you'll find that there's something familiar there.