I agree with Elm.
Soundwise the E-II has a lot of character ("deep" sound, slightly "coarse", not very refined nor cristal clear) while the E-III has a "cleaner" sound (this even gets worse - or better if you like - with the EIIIX series).
Of course the E-III is more advanced with more possibilities, memory, and SCSI.
FYI: I rarely use the E-III, while the E-II is always connected in my studio.
Both samplers are not reliable. Especially if you transport them (even on a soft surface on the backseat of a car), but in case of my E-IIs they even get unreliable by just sitting on a table
The E-II is suffering from all kinds of bad/weak contacts (IC sockets, board and ribbon connectors, buttons...) so be prepared to open the unit from time to time to push some ICs and unplug/plug connectors.
The E-III is suffering from weak voice circuits. Mine has one voice which is distorted, and which I - nor another synth technician - have been able to repair. Fortunately you can disable individual voices in one of the master settings menus (this can be done in the E-II too). In my E-III the distorted voice has been disabled for 2 years already; it's a 15 voice polyphonic sampler now
Knowing that both samplers are inreliable, it's good to know that the E-II is "service-friendly": it's quite easy to service the unit and to repair it.
The E-III on the other hand is a technician's nightmare. It has not been designed to be serviced. The way the PCB boards are mechanically installed in a kind of "plug-in tower" makes it impossible to quickly trace/find problems with meters and oscilloscopes: none of the electronic components can easily be reached with probes. So often the technician has to remove and disconnect one or more of the boards from the tower, solder some wires on the points that should be measured, reinstall the boards, power on the sampler and do the measurements on the wires. And this over and over again until the failure has been found. In practice this means that synth technicians need a lot of time to do some simple checks, which results in high service costs.
My advice: go for an E-II. And avoid the E-II/HD versions, go for a normal E-II or E-II+