I use both services, but one thing that really sets Gog apart is their strong stance on no-DRM titles.

If my internet is down (it happens often enough, since I live out in the country), games on my Steam account will soon be unplayable, either due to "Steam is not able to access the key server" or due to "Steam needs to update. Please go online". It's a form of DRM, no matter how you cut it.

Gog, on the other hand, lets me play my games whenever I want whether or not I'm on the internet. They also throw in a lot of free extras like the original manuals, soundtracks, expansion packs, etc.

A typical day on Gog is like "Hey, Alpha Centauri was just updated and now it includes Alien Crossfire. Go download the expansion for free."

A typical day on Steam is like "Hey, sorry you weren't able to play your games for the past 12 days because you were offline. But in the meanwhile, such-and-such came out with a new expansion. Go pay $20 for it".