Here is an experiment.
Instead of EADG, tune your bass up a half-step to FBbEbAb. If you like it better this way, then you are a good candidate for heavier-gauge strings.
Instead of EADG, tune down a half-step to EbAbDbGb. If you like it better this way, then you are a good candidate for lighter-gauge strings.
I think some of the above posters have it backwards with their description of the sound! In my experience, heavy gauge strings are twangy and brighter sounding with more harmonics, while lighter gauge strings are mellow and deep with a stronger fundamental. You can confirm this with your own ears by doing the experiment I described above.
I personally use TI Jazz Flats on my P basses. These would be considered a "lighter tension" string, I guess. I certainly find them to be quite warm, growly, and expressive.