1. There is no client, purchasing and downloading is done entirely through the website. There is an entirely optional downloader, if you want to go that route, but you don't need to.
2. Steam is DRM. Every game you buy from them is basically a rental and your ability to continue using those games is entirely under their control. GOG does not have DRM. You buy a game from them, it is yours to use unrestricted forever... literally.
3. There are many games here that are not available at all on Steam, plus all of GOG's games come with additional extras like soundtracks, concept art books, behind the scenes videos, wallpapers, avatars, etc that Steam does not offer at all or in some rare cases, offers at additional cost.