Read someone say that the GOG version runs way better? Is this cause the game doesn't try to connect to the now shutdown "My Steelport" servers?

edit: oh, sorry. You didn't mean the remake ...
Both Steam and GOG version of the original did run just fine on my old PC. On the current one it doesn't matter anyway.

I know that I miss being able to save character designs in the GOG version, that feature is only available on Steam.

You could try to add the offline emulation for steelport to your computer to see for yourself.