I would take the newer model for these reasons:
Graphite reinforced neck
String through body bridge
Rolled edge fingerboard
Over the years I've owned a 73,76,89,and 97 jazz bass. The ones made since the late 90s are the best in my opinion. About the older bass, unless the seller is selling you a 61 reissue, what he may be talking about is the body style. In the late 80s Fender slightly changed the body styling to incorporate a 22 fret neck, many players refer to this as the "boner" bass. I would avoid this model as necks and body's are not interchangeable and, in case of catastrophic damage, irreplaceable. Around 96, and I could be wrong about the dates, Fender went back to its "vintage" styling, with 20 fret neck and the traditional body. Somewhere in there, they began to use the upgrades listed above.
As far as choices go, with the newer bass, I know what you've got, and it's good. As for the older bass, it could be great, but you, or he, is not giving us enough info to give you an answer.