Does the GOG version of BG3 run better than the Steam version of the game?

Its the exact same underlying code, the only real choice your making is whether you want to by a perpetual license from GOG or a rolling software lease from Valve

I am genuinely curious, what made you think there'd be any real difference in running the two versions? Did someone suggest the GOG version runs better?

That could actually happen if the Steam version had Denuvo, however Larian doesn't really do DRM even on Steam.

What?!?!? Can you think of a single game that pays for Denuvo and a GOG release?
That would have to be the dumbest publisher of all time. No. They are the same game and it's demanding of the CPU.

Rime made quite a few headlines with regards to performance, allegedly because Denuvo.
Don't know when it came to GOG though.

With Denuvo and other DRM methods prevalent, its been shown to make a difference.

Outside of that, unless they compiled it differently, no it shouldn't. Though i suppose they might have a different build that includes a bunch of specialized CPU instructions, and one that's totally generic, and a download is done based on detection on the store page... (doubtful).