As the title suggest, I am looking into which version to pick this time.
Any downsides outside of not being able to use steam friends for multiplayer?

Direct connections and LAN play are supposed to work platform independ. Any real differences beside steam friends invites into games?

No downside. Direct Connections and LAN play doesn't care about what platform you bought the game from.

I pick GoG for games that are sold on both because I like to have better control of what version of the game I am using and the ability to go back to a previous version if a new version ends up being problematic for me. I also like I get to keep an installer so if GoG ever goes down I still have the game regardless and can install anytime I want, Steam doesn't give us that option if Steam ever goes down.

GOG - more personal control over updates and ability to roll back.

Steam - Workshop. If you like mods and other add-ons, Steam is way ahead of Nexus because the tools make it very simple to publish.

Otherwise, not much difference. I own both and use both.

Would you mind to elaborate on nexus? What is nexus? A tool? A website installing mods for DOS2?

edit: ok googfu. Nexusmods.com

https://www.nexusmods.com/divinityoriginalsin2/mods/searchresults/?src_cat=1

Seems like steamworkshop has over 400 mods, while nexus has only about 100 mods. Though there seems no need to modify anything to make the mods compatible with the gog version, so it is merely a publishing issue.

One of the most important aspects has not been mentioned: GOG is DRM-free. Always. That's a huge plus in my book and I do everything to support that.

Re: Mods: Nexusmods is an excellent platform for mods. Sure, some modders may not publish on there but after the various catastrophes that Steam Workshop (along with others) practically invited by trying to monetise mods and doing little to stop people from stealing free mods and making bucks off them, I think more and more will find their way back there. Nexus is just one of the major hearts of the modding community and one of the best places to cooperatively push the frontiers of mods in games.

I bought from GOG and have yet to find the Divinity Engine 2 Editor.

Look under backups and goodies.