If you couldn't run The New Frontier on Steam without upgrading your machine, it's unlikely that the game will run on GOG. I believe that the underlying system requirements are the same for both versions.

You might get slightly better performance on one or the other (many GOG games run better on my very old PC as they don't require the steam client running in the background), but if you can't start the game at all due to high system requirements, buying the same game from a different store is unlikely to fix your issue.

Hope this helps.