I've owned or still own a number of Japanese Fender basses and none of them have ever disappointed. And while I've never owned one of those lovely Walnut JB62's, they've long held a spot on my personal GAS list. So, if it were my money to spend, that's the one I would get.
On a basic level, the physical specs should be pretty close between them, except perhaps the weight. (If the JB62 is made of basswood, it should end up being a bit lighter than the alder Flea Jazz) Fender-Japan loved to use a mix of '70s and modern specs for their Jazz bass necks. I guess you could almost call them a "Slim '70s" style…a vintage, 7.25" radius, but with less front-to-back thickness.
P.S.: Even if it's listed as an FSR model, Fender-Japan sold this model for a handful of years. Technically speaking, it's a standard, "Japan Exclusive" model, not a Factory Special Run. I believe it's model designation was "JB62 WAL".