As of the moment I
believe the amp models are in parity across all the Fractal Ax* hardware.
As for effects differences, some that come to mind off the top of my head...
III has tri-chorus, II does not
III has the Multi Delay block split into three different blocks (Multitap Delay, Plex Delay, and Ten-Tap Delay), which have additional
features (for example: enevelope following, ring modulators and chrousing on delay lines, quad parallel and quad series delay types, etc) not available on the II
III Enhancer block has an added “Steroizer” mode
III Input block noise gates add EMI filtering
III Pitch block has 4 voices and a new faster/better pitch detector
III has additional improved Reverb algorithms
... and of course the III allows for double the number of blocks and double the channels of almost every block in the II.
All that info and more can be found by perusing the “Sounds” portion of the wiki:
http://wiki.fractalaudio.com/axefx2/index.php?title=Category:Sounds
Also of interest might be this article which is a broad overview comparing features of the III to the II:
https://wiki.fractalaudio.com/axefx2/index.php?title=Comparing_the_Axe-Fx_III_to_the_Axe-Fx_II
... and the effects comparison table:
https://wiki.fractalaudio.com/axefx2/index.php?title=Effects_list#Effects_comparison_table