Cab Pack Wizard
So I wanted to play through the Axe-Fx III and the Axe-Fx II with quick switching to really compare the playability and feel side by side and came up with this preset that allows me to do so. Here's a video of me comparing some amps and different settings.
The end result was that "maybe" the Axe-Fx II is a bit more scooped than the Axe-Fx III. The Axe-Fx III's compression is a tad more natural sounding to me but at the moment they're very close to each other when using the same IR.
Check the video for sound samples and more information.