I have a BB735, which isn't quite the same of course, but I can share a few observations I've had over the last few years of owning it.
First of all - I love this bass. I have a Mexican Fender as well, but it's a much older passive PJ model, so not a good comparison to the modern Fender. But I measured once and found that the bridge pickup on my Fender is a bit closer to the bridge than it is on the Yamaha. I don't like the Fender's bridge pickup, it's too tight and nasal, but the Yamaha being a little further away gives it some more growl. As someone else noted above, it is a single coil so you'll get some hum on it that the Fender's noiseless won't have. But overall I find the bridge pickup on my Yamaha useful in a way that my Fender's bridge pickup really isn't, at least to me. I think they blend together really well and I like the blend knob vs the two volume knob setup my Fender has, but it looks like the Player 2 Modified Active has a blend pot, so for you they're the same in that regard.
I have also found that it's easier for me to reach the upper frets on my Yamaha than on my Fender. The neck joint is sculpted on the Yamaha, while the Fender has the typical squared off one. The Yamaha also has a little more room between the neck and the lower horn, which for me makes the difference between being able to comfortably fit my hand in the space and getting stuck as I do on the Fender. But that's only an issue if I'm playing way high up.
Speaking of neck joints, the Fender again has a typical 4 bolt attachment, and while there's nothing wrong with that, the Yamaha has the same four bolts plus two more that go in at an angle, pulling the neck down snug into the pocket. In theory this gives it a tighter fit. I do think my Yamaha has better sustain than my Fender, but again there's age of the instrument to consider. However, the BB734 and 735 have a layer of maple sandwiched between thicker slabs of alder in the body, while the Fender you're looking at is just alder. This does add a little weight to the Yamaha but even the 5 string version I have is pretty comfortable to play for long stretches if I use a thick leather strap.
The bridge on the Yamaha has a couple neat features that the Fender lacks. First, the saddles on the Yamaha are reversible, with one side being rounded and the other having a sharper corner. I have my B, E, and A strings on the saddles with the pointy side up, it doesn't make a huge difference but it does give them a little more definition. The Yamaha bridge also allows through-body stringing as well as top loading, and the through-body method goes through the body at an angle, which makes thicker bass strings less likely to snap than a 90 degree angle.
TL;DR summary, since I realize that's a lot to read:
Points in favor of the Fender:
- Noiseless bridge pickup
- Probably lighter
- Bridge pickup closer to bridge, if you like a tighter, brighter sounding bridge pickup
- Fenders are cool and recognizable
Points in favor of the Yamaha:
- Better neck joint
- Better bridge design
- Bridge pickup closer to neck, if you like a warmer, more growly bridge pickup
- 3 layer body design with a layer of maple = loads of sustain
- Easier access to the upper frets (maybe, depending on the size of your hand)
- Better reputation for quality control
If it were me in your position, I'd go for the Yamaha over the Fender, but if you prefer really bright bridge pickups, have smaller hands, and are bothered by single coil noise on the bridge pickup, I don't think you'll be dissatisfied with the Fender.
), and the shape of the body appeals more to me, maybe just because of popularity rather than anything else 
