For our TP playback purposes, they are very similar. The III has "better" components in the audio board for certain.
Functionally, the IIIs do have better tape deck control with smoother operation even the feel of pushbuttons have been improved. The III's reel turntables have the spring loaded spindles that can be used with more modern NAB hubs from other brands including the fancy Revox NAB hubs with multicolor metal flanges. On the other hand, the hubs for IIs have to be Otari or VIF types for straight spindles.
The bigger difference between two models for audiophiles is - unless a III is ordered with the "P" option for 4 track repro head, it will only have 2 track record/repo heads whereas the II will have the 4 track repro head along with the 2 track record/repro heads in the standard headblock.
I like the sound of a properly aligned II as well as the III and can't tell much of a difference. Thus it is my opinion that the choice comes down to preference of having the four track repro head in II or more modern control scheme on III with less emphasis on sonic characteristics between the two.