For many games, users (and, in some cases, even devs) post changelogs in the dedicated forum for that game or series. However, this is rather hit-or-miss, since not every game has fans (or devs) who're semi-regular GOG forum users willing to repost each new changelog there.
The most reliable way would be to visit the third-party GOG Database, search for the game in question (and make sure it's the entry whose "Product type" is "Game" or "DLC", not "Package"), and select the "Downloads" tab. You can see the version numbers for the offline installers there. (The "Changelog" tab can also be useful.) I don't know if there's any way to see the actual version number for the Galaxy build, but it should always be either the same version as the standalone installer build, or newer. EDIT: As Catventurer points out below, there is indeed a separate "Builds" tab that has version info (though I suspect the naming/numbering of these client-delivered builds might sometimes be different from Steam's, even when the content is functionally the same). I don't use Galaxy, so I guess I became so used to ignoring that tab that I forgot it existed! XD
(There have been cases where the self-contained installers for a game have lagged behind the Galaxy build for weeks, but I don't know if there are currently any such cases. Generally speaking, Galaxy gets updates first [since they don't have to go through the extra packing and verification stages that offline installers do], then the installers come within a day, or -- normal worst-case scenario -- a few days.)