What flavor LP ya got?....if you have a Classic, the pups are ceramic, a different sound from alnicos on the Standards, Customs, Studios......some say the ceramics are muddy....some older (and re-issues) gits have P90's or Burstbuckers, or PAFs.......and they all sound different and have different degrees of clarity....
Keep in mind that tube amps were the only amps available when LP's made their mark on sound, and may be why Gibson kept changing the pups...different tones for different ears.....messing with the controls on your amp will go a long way in changing the sound of single coils vs the buckers your probably have on your Paul....gibs