Just recently, I have installed the GOG version of Fallout 3 onto my computer. Now I want to transfer the mods from the Steam version to the GoG version.

What folders would be recommended to transfer, and which ones do not? Especially when it deals with Texture Changes to the game.

Are you using the Fallout Mod Manager (FMM)? If not I'd recommend grabbing that, it makes installing mods much easier, irrespective of the version you have.

I don't have F3 installed atm, but it should be similar to NV (I know FMM works for both), in which case you'll need the non-standard .bsa and .esm files, which should be located in the \data directory of your F3 installation. I guess the best way to do this (without downloading all the mods again) is to copy them from the Steam version to the location suggested by FMM - then run FMM to configure the mods you want (and their order) and it should copy them to the right spot.