I have an '04 Mexican Jazz and a 2000 Mexican Precision. The Jazz feels really good, well put together, nice finish, lovely neck, the only problems were with a funny neck pocket, average pickups and crappy bridge. The neck pocket cut isn't a big deal, just a bit unsightly, and the pickups and bridge were easily fixed (SD Quarter Pounders and a BadAss II).
The Precision I bought second hand. I don't know how much that contributes to the following, but probably not a lot. It doesn't feel as good quality, the neck isn't as nice (and that's not just a Precision/Jazz difference thing, it's really not as nice), and the pickups were even weaker than the Jazz's. It's probably equivalent to the Squier Std P-Bass Special in my local guitar shop. They were built about 4 years apart so that might be a contributing factor.
I tried similar Precision at the same time I was testing out my Jazz, and that was very good, but it was the day after my 18th birthday, so in my hungover state I wasn't really prepared to handle to the weight of the P
Wandered a bit off topic there! Anyway, my point, hard to find in all that, is that MIM stuff can vary greatly. I'd put my Jazz up against a MIA or MIJ in terms of quality any day. The Precision has the same mods as the Jazz, but it's just not as nice. It [i]is[/i] a good bass, but it doesn't have the same feel. The sound though is great with the new pickup and bridge, really full and meaty, but the build isn't as good. Just my 2p there.