To some, this response may seem crazy. IYKYK.
As a life long Precision player and an owner of many Pbasses, I will tell you that Leo's design is remarkably reproducible sonically, provided; you stay with a well worn selection of tone wood, put a split coil in the exact position and use a 34" scale. These elements are far more determinant to the sound than the strings, what company built the bass or what it costs.
If you play a batch of the exact same model, from the same factory and there will be some that are really good, and some that are just better than the rest. (we will assume that QC has weeded out the dogs, but in the real-world, that is not always the case). Always a good idea to play several if possible.
My friend, Ed Friedland, the Bass Whisperer, demonstrated how similar a Pbass from several manufacturers, with many types of strings, at different price points sound, especially in a mix. Listen and see/hear for yourself.
If you want to spend a lot of money and buy a Fodera P, or a Lull P, etc., by all means, buy one. We are on this earth for a very short time. In a mix, you might not be able to hear much difference compared to a Fender Player Precision. In fact, of the many Pbasses I own, the best sounding, most resonant is a Player P and the least expensive.