I don't know too much about Edinburgh College of Art but I can tell you about CSM as I attended there.
CSM is a great school, it's very conceptual and really promotes the overall idea than the final outcome. It is primarily driven by graphic design and fashion—and they do both of those very well. It's a bit too competitive for my liking, but everyone is wonderfully talented and you'll learn just as much from the teachers as from your fellow students. By the way, they are making a big move (this year or next year?) to a new site at King's Cross. They're trying to merge all the CSM buildings across London to one site, which I'm not exactly happy with. In my biased estimation, I'd say choose CSM. More exhibition opportunities in London, more networking, more concentration of incredible artists from all disciplines. Hope this helps.
