I don't get the question in a way. You have two basses, one has much louder/hotter output so of course it has more "oomph".
A lot of amps have a button that cuts the input for active basses, something like -10db. Leave it out for passive basses.
You'll have to adjust the volume and probably eq to get them in the same ballpark when switching back and forth.
I have two passive basses, one with much hotter pickups, so a similar issue. Volume on 10 on the jazz is like master volume on 7 on the Guild (leaving the amp volume the same).
A lot of amps have a button that cuts the input for active basses, something like -10db. Leave it out for passive basses.
You'll have to adjust the volume and probably eq to get them in the same ballpark when switching back and forth.
I have two passive basses, one with much hotter pickups, so a similar issue. Volume on 10 on the jazz is like master volume on 7 on the Guild (leaving the amp volume the same).