Zoom G3X for me. It lives in the bottom of my duffle bag, so compact that I forget I have it with me. I actually quite like it, for what it is. Every so often I'll boot it up and revisit the patches and tweak a little bit. In fact, I was just recording some samples the other night so I could tweak the G3 to get it closer to the Axe Fx, which I haven't done yet. But at least you can hear where I'm at so far. I was also comparing it to another backup option. I just get the Atomic Amplifire, although it's three times the price of the G3. I think the G3 may actually have more effect options, and I like that the G3X has the expression pedal built in. Anyway, this sample has the Axe Fx first, then the G3, and then the Amplifire. It's just a little short clip of the riff from "Slide" by the Goo Goo Dolls. I just happened to be testing that patch.
I leave my G3 in the mode where you can scroll up and down between patches, rather than the mode where you can turn effects on and off. If you are handy, there is a cool website that explains a bunch of mods you can do to the G3.
AshBass Zoom G3 and G5 Mods and Information
I also think that the G3 is a better choice in that it's spending $200 on something you most likely will never use. Before I got that, I was carrying around the Zoom MS-50G. It actually sounds identical to the G3. If you only need one or 2 sounds, that may be a better option. I wanted more patches and an expression pedal, which is why I switched to the G3.
But, at the end of the day, the Axe Fx is the only thing that gets used.