The Fender American Vintage Series Reissue instruments are built to the same specifications as the original instruments using new "vintage correct" parts. Fender does a pretty good job in producing an instrument very close to how it would have been if you had bought a brand new one in that year. I tend to believe that, due to improved manufacturing techniques and tighter manufacturing tolerances, the current AVRI instruments are likely BETTER than the original. Many say that the AVRIs are the best non-Custom Shop instruments that Fender produces.
The Fender Japan reissues are what I like to call "MIJITSO" (Made In Japan In The Shape Of...). The 57 P, for example, has many of the same cosmetic characteristics as the original, but misses on the little details. It doesn't have the "reverse" tuners, or an anodized 10-screw pickguard, and uses poly instead of nitrocellulose lacquer. The pickups (at least the "USA Vintage" ones they use for some models) sound VERY good, but aren't quite the same as the AVRI. All that said, the Japanese Fender instruments are built and finished REALLY well and are consistantly very good instruments at real-world prices. If you don't care about being exactly "vintage correct" a MIJITSO is a great choice.
The one thing that the the reissues lack is the "mojo" of decades of making music in the real world. If you want that, it'll cost you MANY thousands of dollars for a real one.