Originally Posted by The Dark Wolf
So far, the main differences that stand out are: the GNX3000 can get some really amazing sounds, but it requires a TON of tweaking and adjustment, and it sounds 1000x better through the effects loops of a tube amp than it does direct. The Axe-FX, however, just sounds amazing right out of the box. You can tweak the Axe-FX much much more than you can any of the GNXs (even down to things like which mic is in front of the cabinet, graphic EQ, the precise way/order that the amp(s), cabinet(s), and effects are linked together, and settings for each that get much more detailed than anything you could actually even do on the real amp or effect -- the virtual amps even have virutal power tubes and virtual transformer tubes). So, you have to know a lot to tweak either the GNX3000 or the Axe-FX, but it's a lot easier to get totally amazing sounding stuff on the Axe-FX than on the GNXs. Also, the Axe-FX sounds amazing both direct and through an amp.
I plan to keep using my GNX3000 for band practices for at least the next few weeks (and I'll be using the GNX3000 at the next two live shows my band has), but probably in a few weeks, I'll bring in my Axe-FX and see how that goes. The GNX3000 is a lot lighter, easier to carry around, smaller, more compact, and with a good tube amp with an effects loop, it sounds amazing.
One thing I've noticed when playing through clean and low gain settings is the really natural "organic" sound the Axe-FX has. This isn't the type of thing anyone would notice live, but on a recording, it's very noticeable.
Edit: I'm thinking of getting this for a pedal board: