I like all of the options available with the Axe-FX. You can go into the P.A., headphones (with the II), into a computer, use power amp/cab, use just powered speakers, etc.
Everyone, especially all of us tone junkies on RT, know that being able to replicate an entire tube rig is difficult. I can't afford to buy the Fender Blackface, Modded Marshall, Mesa, etc., etc. so the Axe-FX II allows me to dabble in all of those and I really enjoy it. Sometimes I'm in a blues-tone type mood and sometimes I want to play heavy stuff. I like having all of the options.
There is a difference between the modelling of the past and what Fractal has done with this. Years ago I had LINE 6 amps, Johnson Amplification, Behringer V-AMP, etc. and although they sounded cool, it did sound like a modeller and just a louder modeller as you turned up the volume. You can hear that improvement with the Axe-FX.
Maybe folks that have just started playing can't tell the difference. I've been playing since 1985 and can definitely tell the difference.