If you have Steam set to auto-update, then the delay with GOG creating patches will sometimes make the two temporarily incompatible. Other than that, though, it should work.
Did you try a Direct Connection using IP address and Server ID (can be gotten after starting the game in the Connection Menu [diamond icon top of mini-map])? A couple people have mentioned using the LAN connection with VPN software installed (Hamachi, Tunngle, etc).
Please email supportdos@larian.com, with a description of the problem and the report.zip file generated by the
D:OS support tool (for the PC version), for both systems. The report will contain system and network information, any crash dumps, and your saved games (which are not relevant in this case, and can be deleted from the zip, if file size is an issue.