So, after downloading the game via the steam client there is no difference between versions (Larian Vault, GOG, Steam)?
Well, only the Steam version can use Steam features (invite/connect via friends list, Steam workshop, etc).
The Larian Vault version is essentially the same as GOG, a full DRM free install package download, and patches to update (eventually being rolled into a new full install).
Steam will get updates fastest, because it has the fastest and easiest system in place to distribute updates. After that, immediately after release Larian will focus on the GOG version first, since that is the next largest group of players.
You can get mods through the Steam workshop and transfer them to non-Steam versions of the game (mods are just sets of files in a certain folder), and there will be other places to get mods (Nexus, etc).