Right now I'm running my Strymon Brigadier stereo into my Styrmon Bluesky which goes left to my Laney VC30 210 and right to my Blues Junior.
I set the VC30 to have a Blackfaceish tone with no mids and I roll the bass off the junior entirely to get a "scratchy", "radio" tone.
They blend together REALLY nicely and I can either use them as STEREO or as a mono, single, richer amp tone.
I think you have a couple of options.
I'd recommend something like the Radial Bigshot (
http://www.musiciansfriend.com/amplifiers-effects/radial-engineering-tonebone-bigshot-aby-passive-switcher).
It's an AB/Y switcher. So you have amp A with FX, amp B without and you have the option to use both amps with or without FX on amp B.
You could also use a loop switcher like the Carl Martin Octaswitch and have the amps set to 2 loops (with send and no return) and then you can select which FX/FX combination go to which amp/amp combination with the dip switches. The Octaswitch, as the name suggests, offers 8 preset options.
http://www.musiciansfriend.com/amplifiers-effects/carl-martin-octa-switch-mkii-effects-switching-system
You probably also do it with a clever MIDI rig too.
I really like mine in stereo and (right now) I'm not interested in doing any A/B/Y work because then I have to take 2 amps to gigs. My stereo setup is easily set up for recording though and in the case of playing at festivals they often have a couple of amps spare. I think stereo only really has its uses in studio/recording environments where it's really perceivable.
What would be killer is a Princeton for clean, a 57 Deluxe for dirty and a BigShot for switching. Never need an FX pedal again?
EDIT:
I forgot to mention that my Rickenbacker 620 has stereo capabilites and the tone and uses from using a different PICKUP for a different amp is quite a different thing. For one thing, you can have your bridge pickup always on an overdriven tone and your neck pickup on a pristine clean, reverby sound. Or visa versa. Also the combination pickup setting sounds really interesting between two amps. I'm also suspicious of splitter cables sucking tone. Would love to find a good quality stereo cable and then get a 1x stereo to 2x mono box made for splitting purposes.