The Axe-III needs to have 4x4 re-amping, convolution reverbs & better overall effects & drive/fuzz pedals, tone matching at least as good as Ozone(No,the Axe-II TM is not as good!), cabinet IR's taken to the next level(whatever that is, but there is obviously still room for improvement).
Also no need for 'tonal' firmware improvements because the tones should have all finally arrived!!! This will mean that patches/presets/tone matches will always sound the same as you made them. Firmware updates will only add additional amps,effects,features & bug fixes!!!
Until at least 99% of these things are possible, don't bother with an Axe-III......