I bought (and returned) Arkham Asylum on Steam and failed to get it to run. I ran into the typical .net errors.

Is the GOG version any different?

Quick specs:
Window 10 Home (1904), 8 gb memory, AMD Phenom II X4, Radeon R5 230 w/2gb

Thanks

Arkham Asylum from GOG seems to work fine here, with no .Net related errors.
I play it on a Debian Sid (Linux) with WINE, so your experience on Windows might be different,

GOG version is better/easier to install and get working.

All I needed was to add some DX additional libraries:

https://www.microsoft.com/en-us/download/details.aspx?id=8109