I also have a Squier JB modified. I first replaced the electronics by a sadowsky VTC preamp (4 knobs). It requires to move the jack to the side of the body, so I had someone do it for me for 50 euros.
It was a great improvement, but I still lacked some definition, especially on the B string. My bass teacher plays a Sadowsky and the comparison was cruel to me. Hopefully, I came across a set of Aguilar AG 5J HC pickups on a popular french classified adds website.
So I bought them and installed them. Honnestly, it was worth the money... I now have a very very nice sounding instrument for less than a thousand euros. The Sadowski might still be better, my bass has a better quality over price ratio ;-)