If the MIM Fender is a Classic Series Jazz ('60s or '70s) I'd probably go with the Fender.
Classic Series is quite outside the budget. All things being the same the Sire is going to be the road of least resistance. Before I found the Sire my focus was a Squier VM of some ilk.
Funny that the Classic Series was mentioned. I was going to say…
If it were my money, I'd go with a Vintage Sire. It shares a lot of physical specs with the Classic '70s Jazz…a bass I owned and really, really dug…at about half the price. Plus, you get a very tweak-able preamp system along with it.
I'll admit that, as a strictly-passive guy, the preamp is kinda intimidating, but that's not necessarily a deal-breaker. If I couldn't wrap my brain around it, I could always disconnect it, rewire it to passive and I'll still have a bass with specs I prefer.