Tube amp with a Tube Screamer - question about it's behavior.

the preamp circuits are completely different between the two amps.

they will react to a boosted signal differently.

it's partially a 'preamp headroom' issue, partly a 'gain structure' issue, and partly a power amp 'headroom' issue.

this is part of the magic (or pain in the @ss) of mixing/matching effects to tube amps.

it's part of the voodoo, and this wonderfully illustrates why what is good for the goose, is not always good for the gander.

FWIW.....
if it were ME...
and i wanted to keep the two-amp combo...

i'd get a treble booster, or clean boost, for the Vox....

keep the tube screamer on the Fender.....
and tweak them both separately until you get them at the same volume.

the way the tube screamer works, will react completely different between the two amps, better not to settle on a compromise setting between the two, better to commit the pedal to one amp or the other....

more shortly......

Here's some fun stuff. Some pedal makers make an a/b/ab pedal. I have two Blues Juniors in my collection of amps. One of those pedals is great to have around. You set one amp for clean and one amp for distortion and switch between the two. Old School Channel swithing! Then there is another button that allows you to have both on at the same time. It sounds great when you have the edginess of the clean sound combined with the fat mid distortion! This also works well with unmatched setups like yours. Many of the tracks you hear on classic rock recordings were actually done this way. Not just one amp, but a combination being recorded at the same time. Depending on the cabs and speakers, this can sound HUGE! Just a tip from a guitar player.LOL! 

Also try the reverse. The Vox can be very chimey when overdriven while the Fender lends a little more bottom fatness.