Shaggy mane has a whiter, shaggier (more floccose) cap, and the cap margin curves toward the stipe when young, making it look completely oval in cross-section. At least that's my observation. This is a genus (actually several unrelated genera) that I have not eaten. Too many opportunities to confuse things with the alcohol inky which would ruin my average week.

Tom Volk's page on Coprinus mushrooms is pretty great: http://botit.botany.wisc.edu/toms_fungi/may2004.html