Truehare: I think the XBox One controller works too - no reason not to, if the DS4 works, right? - but haven't tested it yet.
I don't own an Xbox controller so can't confirm, but there IS a reason why it wouldn't work.
Controllers like the DS4 use a protocol called DirectInput, whereas controllers like the Xbox controller use XInput. XInput was introduced in 2005 alongside the release of the Xbox 360 and it has since become the standard protocol for Windows, so any controllers that are designed for use on the PC, including the Xbox controllers, use XInput. The DS4 however uses the older DirectInput standard, which is why if you want to use a DS4 with most PC games, you need to run an application like DS4Windows to basically trick the PC into thinking it's an Xbox controller.
Blood Omen was released in 1997, some 8 years before XInput was introduced, and therefore did not support XInput at the time of first release. I'm unsure if GOG's wrapper they use to make the game run on modern systems includes XInput support or not, but if it doesn't, it's entirely possible Xbox controllers wouldn't work just straight out of the box. I guess it depends exactly how close the game is to the original PC release. The game has no issue using a DS4 controller without any mods applied, meaning it definitely supports DirectInput, but I'm unsure about XInput.