GOG gives you access to a single file (for FS2 anyways) to download and run to install the game. (That's unless you decide to use the GOG Installer for which there is an option on the website; I haven't used that, it might be easier or harder, not sure.) There is no DRM (aka nothing snooping around trying to make sure you didn't steal it and it will install on any machine that you copy the file to without hassle).
Yes, the Installer would work on the Steam version of FS2. Steam is a bit more restrictive as you have to have Steam and be logged into your account to install. The Steam install of FS2 also has a bug that (last I remember) requires the user to download and run a .reg file to patch the user's registry, as the Steam FS2 install doesn't do this correctly.
I would honestly go with GOG. They also have many older games that are patched (correctly!) to work with modern OSes (like a lot of the Star Wars games, X-Wing, TIE Fighter, XvT, X-Wing Alliance, Rogue Squadron, a bunch more that aren't space sims, just to name the ones in the Star Wars universe, plus a lot of the Wing Commander series).
If you have a choice between getting something on GOG or Steam, pick GOG every time. I like Steam and have a ton of games with them, but GOG is better as far as making sure their games actually work.
If you are stuck and need help getting your version of GOG FS2 to install, I'd be happy to guide you.
For a start, once you've purchased it on GOG:
