Personally I would not change the gauge to fix this problem..
As far I am concerned .100 is the smallest E string you want to use if you still want to call yourself a Bass player

OK..just kidding..some Rics sound thier best with a .095 on the E such as Chris Squire uses...
Getting back to your problem....you need to first isolate this problem...Thier are basically three catagories this usually falls in, one is the String, second is the phyics of the bass, third the electronics/pick-ups....
If you changed strings then that rules that out....
Next you will need to put your ear to the body and play all notes including E-string notes...you are listening for resonance or lack of...ie, destructive tones occur when standing waves bounce back from a part of the bass, such as the headstock via the neck/truss rod and create dead spots...
If your bass sounds great in the body...then you may need to look elsewhere...
I have seen cases "from the factory" were the bridge saddle was cut slightly off for one string...This caused the string to be off aligned from the poles in the pick-ups...even being slightly off can be a significance in signal amplitude for that string.. Can you adjust your pick-up heights to compensate for this??
DOes your problem occur with both or either pickups???
Is it more pronounced using the neck pick-up???
Is the open E-string a problem as well?? Or is it only fretted E-string notes that drop in level???
I have seen some basses with this situation...where the E had the lowest energy.... One solution was to use a stainless string only for the E ....and keep nickel for the other 3 strings...
Other situations just similair..after investigating...were linked to the the way the nut was cut or the way the bridge saddle was cut...ie, the E-string was not sitting nicely in the grove of the saddle...depending on what gauge the saddle was originally cut for...the string may have a small gap below it in the saddle..ie..the conturing of the saddle to the string is critical....also look at the back angle behind the saddle..How deep in the saddle the string is also important..if the string has any longitudal movement when it is struck..it can kill the natural vibration...
Best Luck
Chris