My observations based on my experiences, as useful/less as they may be, are as follows.
Stock Squier Jazz bass (VM70s).
Sound: Very clinical, but passable for a jazz. DD pickups sound better than newer Fender ones. Potentiometers are 500Ks and really thin the sound of these out dramatically.
Fit and Finish: Well done, within specs, fretwork was acceptable, required very minor fret filing to get the string height I desired, which was lower than standard. Pickup and control routing was very clean.
Recommended upgrades: Shield the cavities. Change the 500k pots out for 250s (or do what I did and drop a Fender American harness in from another bass that I'd modded), and that will open up a whole lot of meat in this bass. Change out the cap for something a bit more strictly controlled in terms of quality control and your sound consistency issues in terms of tone may narrow appreciably. Other than that, I'd leave it be and gig the pants off of it (and I have).
Stock Fender MIM Jazz bass:
Sound: Good. Typical jazz bass, with great single-coil tones no matter what you pull down or up in terms of pickups.
Fit and Finish: Again, very good rigging, but the control cavities and pickup routing was a bit rough, and made shielding a bit challenging.
Recommended upgrades: Shield the cavities. Upgrade the pickups to something like Barts, Dimarzios, Seymour Duncans, etc. Stock pickups are fine, but you'll get a lot more out of your setup with upgraded pickups that can pull nuances better than the stock ones. Controls are fine as they are, but Varitones and Parallel/Series switching can really make these basses (and the Squiers and the MIAs) tone monsters. My favorite is a Stellantone Elek-Trix. Dipswitch selectable capacitor value, and a push-pull parallel/series switch. I'm not affiliated with them, but I loved this plug-and-play harness a lot.
Stock Fender MIA Jazz bass:
Sound: Very similar to a MIM Jazz.
Fit and finish: Very good. Routing seemed pretty nice and shielding went it well. Someone ran a sander through there.
Recommended upgrades: Well, you can keep it like it is, and it certainly won't hurt you, but upgraded pickups and perhaps some pickup switching capabilities would be welcome in most jazz basses. Aaaaaaaaand shield it, too.
Overall
Sound: They all sound good, but stock, it's MIM=MIA>Squier. Now, if you mod the controls on a Squier, however, it's MIM=MIA=Squier. They can all get the job done very well.
Fit and Finish: For me, it's Squier>MIA>MIM. It's just what I've experienced. I've seen a lot of each of these, and the Squier string spacing, tuning alignment, nuts, and fretwork were all well within what I would expect of a competent mass-produced bass, especially the more recent models where QC was really stepped up. MIAs and MIMs are just as good, but the control cavity cleanliness is my biggest pet peeve, because most guys bring them to me to shield.
Recommended upgrades: Preamps, tone controls (like SD Blackouts for passive basses), Varitones, etc., are all very much subjective, but I honestly would recommend a pickup upgrade eventually if you want to hear everything your bass is capable of giving you. Not that Fender is bad at pickup design, but there are better choices out there. And all of them should be shielded, as the factory shielding paint really doesn't get the job done.
Final word?
Look, if you know you're gonna upgrade the bass to really chase your tone, start with a Squier. They are very inexpensive, and set up properly play VERY well. The name on the headstock means ZILCH. If it's a dog, it's a dog, if it's a gem it's a gem. The proof isn't in the logo, it's in the sound.
But if you just want a set-it and forget it bass, hit the MIA or MIM depending on your bucks.