Man, for me, I figure go with the original Fender if it's a Fender-based instrument we're talking about... I know that there are a ton of luthiers/private builders who do their own take on the instrument, but if it's a Fender-style, I'll just save to go with Fender themselves.
Even their new moderately priced Player Series guitars and basses are made well and are a great platform for future mods if desired. As for the question posed, is the USA Fender the way to go, for me, while it's Fender for sure on a Precision style bass, I wouldn't discount the MIJ or MIM models.
For me, I recently picked up two P-Basses... well, 3 (the 5'er was sold here on TB):
1. Fender Japan Limited Midnight Black 60's Traditional P (Basswood, but boy does she thump, grabbed some AV Atlas Pickups for her, yet to be installed)
2. Fender American Elite Precision Bass (albeit with a J in the bridge), she's bad and tons of options
3. Fender American Professional Precision-V (sold, but sounded amazing when tested, only play a 5 with the band)
Here's some Bassporn [pics/vids of each]