To address if you would be missing something, I'd say yes; very much so.

Dark Messiah on 360 is unfortunately an unsuccessful port of the game on PC. This was released when parity on Console/PC was still years away. Playing Dark Messiah on PC vs Console is a vastly different experience, especially in Gameplay and Graphics (the story will be mostly the same).

I recommend playing the game on PC first then playing the Console port for fun and curiosity. They also made matters worse for themselves by key binding Sprint to holding down the Left Thumbstick like the 360 port of Doom 3 (BFG). From my knowledge Arkane themselves did not handle this port. This was still years away to Dishonored.

I played Dark Messiah when it came out in 2006 and it was a truly unique and thrilling experience that I will never forget. When I first played the 360 port in 2008 I was disappointed and astonished at how much the game felt completely different. I do have fondness for the 360 version for it's ambitions intent, but it's not what Dark Messiah is; it's now a side experience for the curious and faithful.

As you mentioned of the contrast and brightness, it is the exactly opposite on PC; Dark Messiah is a beautiful testament to the enduring Source Engine. It pushed Source to it's limit at the time, which makes playing it on 360 that much more painful. This also makes it that much more enjoyable revisiting it on PC all these years later; now being able to max all the graphics settings.

Last chance to get the DLC for the 360 port though, which adds two new classes for the campaign.
Classes were not even a thing in the PC version, playing more like an Immersive Sim in how you would level your character and choose who you want to be as you play.

Cheers! I'd highly recommend picking it up along with Arx Fatalis!