The only way to really know what a given bass truly sounds like take the amp and any effects out of the equation (and by removing the amp and cab you're also eliminating all the variables of the room you happen to be in). Record those basses DI through the cleanest front end you have available, no tone shaping. Track the bass alone and also against something like a drum loop or whatever for a little context if you want, play it back both ways. Listen back on good headphones, studio monitors, etc. How do they sound? Then go from there.
A P, a 'Ray, a Ric--all with weak E strings? Assuming they're set up properly, doesn't add up. Problem might not be the bass....
The problem isn't so much that it's "weak", just more so that the E feels dark and more mushy bottom compared to the other strings.