Don't forget the super useful built in USB audio on the Axe II. Plug in a USB cable to your computer and your directly recording, and even able to do really cool things like record a dry DI track and the effected track, which then means you can play the DI track back and change the amp settings, effects etc. I find it really handy being able to easily record tracks without having to hook up an extra cables etc.
I also really like having the ability to run dual amps, gives a lot of tonal variety and unique tones. Plus, you can run two guitars into an Axe, essentially 2 signal chains, which can be kind of handy if you want a buddy to jam with you, someone on bass etc. I've found that kind of fun and useful too
Last but not least, having the CPU for as complex of patches as you can think up is handy too. Want to run 2 delays, and 2 reverbs, maybe a spring reverb going into a plate reverb or who knows what... you can do it as the II has the power for essentially two of each block.
AX8 is a great unit too, and ideally having both is the way to go, but if I had to be limited to just one or the other, I'd have to go with the II