What's wrong with the Gibson Thunderbird? Gibsons E Bs are short scale, which isn't good for intonation, the Precision was the first ever solid electric bass guitar, and like most of Fenders designs, Leo got it right first time. Precision for me
If I was in your shoes, I would gather up what types of Bands or Styles you like to listen to. If the majority of those Bassist play a P Bass, then that should be your answer.
For overall sound - you can't go wrong with a standardized P-Bass. I like playing the Jazz bass too, but it needs some extra help in some areas in sound where a P-Bass usually does not. -Peddle(s)-
