I do have to ask... have you tried isolating your amp in a closet, and micing it?
I have a feeling the open backed tweed cab style of the Carr is giving you swirly amazing in-the-room sounds which would NOT sound the same as the AxeFx until you start recording the amp.
Its been said before, but I was lucky enough to come to this realization WAY before ever owning an Axe-Fx. I had a Super reverb that sounded AMAZING cranked up in my basement. Just phenominal SRV tone for days. ... until I started trying to capture that sound on record. the second I put an SM57 in front of that amp, it went down the tubes. Very sterile, 1 dimensional. Raspy, harsh...etc. I spent MONTHS learning how to best record amps, but never quite got the super to sound all that wonderful close mic'd.
I tell this story because those months and months of trying to mic an amp gave me the ears to appreciate the AxeFx for what its doing and the sound its creating. This gave me a leg-up on the device because I never tried to recreate the amp-in-room sound.