I have owned a few Jazzes: 68 ( an absolute dog), 2003 MIM Sunburst, very nice, 2006 MIM white, also very nice, 2012 American Special, would have kept this except for financial stress, and now a Squier VM 70s J, which is pretty astounding.
I'm a Precision player through and through, although small hands and, lately, arthritis, mean that that my Precision wears an American Special Jazz neck. So in reality, I'm stuck somewhere in the middle...