I have both these amps.  I've used them with two sets of speakers, the Radial R2s and the IT Radials (you won't find that speaker on this website, it's a Bob Zeigler product).

Both amps work well with these speakers.  If you have a small room and don't need to blast your music, the Integrated will work well with most speakers about 91db efficient and above if there are no complex crossovers to drain a lot of oomph.  The Mark III will allow you to get larger sound levels from the same speakers, and will drive many sets of speakers well.  The Integrated will be just a tad more "laid back" but otherwise the two amps share a rather spectacular clear and involving sound character.