The true and original Jazz bass is passive, so for 'authenticity' all Jazzes should be. The Mexican standard does sound like a Jazz bass (well it is one after all). Although - you will get a better sound if you spend more on a US, how much better it is is a matter of opinion.
Be aware that Fender don't necessarily make the best Jazz basses either, they have long been surpassed in quality by some other brands. The only problem is - none of those other brands say Fender on the headstock... which for some is blasphemy.
And as for the last bass you'll ever buy ? No chance, you'll be lured in and tempted by us lot to buy more .