What is the best bass is completely subjective. Everybody has their own desired tone. In terms of American versus Mexican Jazz bass there are definite differences between them. Build quality of both is quite high. Some even argue that the Mexican Fenders are better built. The Americans have better pickups. They are alinco magnets as apposed to ceramic magnets. As a result they tend to have a fuller bottom end. Most players can hear this difference, and it is why many upgrade the pickups on mexican basses(which can be done for less than $200). They also come with the ability to string through the body. This allows increased string length which provides higher string tension which tends to improve both attack and sustaine. However, most players don't find this difference that dramatic. It is truly a personal opinion which is the better way to go. Try several different basses and find the one you like the best. You might also want to consider something like the Geddy Lee Jazz. It has upgraded pickups, but is not strung through the body. Many players have found this Japanese Fender to be the best option of all.
