I had an EIII and loved it, however they are touchy and fragile beasts and despite not moving mine, I dealt with issues with it.
I acquired a EII+HD over a year ago and love it. It has a character only a EII has.
It has a grittier sound than the EIII, and whatever you sample into it will have that character.
I think the EIII really excelled at real instruments, especially strings. I think of it more as a soundtrack sampler and the EII as a working man's organic sampler, good for inserting into songs to cause the listener's ears to perk up and ask "what was that?".
I would say the EIII has a richer full sound, and remember it samples in stereo.
In the end it is difficult to put into words, for we all listen a bit differently.
If given the choice I would not sell or trade my EII for a EIII, although I love it's sound. Hey it's an E-MU with analog filters.