aside from body shape and neck specs, the main difference is tone. I have/had two precisions to compare to my '81 L1K and the tone is not even in the same ballpark, to my ear. the closest the L1K got to sounding like a precision is after i snipped the cap out that put it in single-coil w/bass boost mode. after the cap was removed, it turned that setting into a standard series mode. while the difference was fairly subtle, it did get it closer to p-bass territory. with that said, they are different animals and should be played side-by-side (if possible) to decide if either is right for you.
I don't play bass, I play stringed percussion.