Shadow The Hedgehog On Xbox 360...?

OK, I know what you all might say when you read this, "Be sure to check the supported games & if the game you have in mind doesn't show up there, then Microsoft nor the Xbox team officially validated the game or confirmed that it works." but still, I want to simply ask & confirm IF the game can be run on the Xbox 360 as I have gotten somewhat mixed answers/results.

As the title states in a nutshell, I've been thinking of getting the game for the Xbox 360. [IF it can run backwards compatibly.] Of course, if it can't run, guess I could always go for the PS2 version. I have done a bit of searching online & a few reviews in an Amazon listing, a few other websites & EVEN a test done on Youtube does confirm that it can run, but I'd like to be absolutely certain.

Since we're on the subject, I also ought to mention that I never really owned an Xbox system at all when I was growing up so this experience will clearly be a 1st assuming I will pull the trigger on this. With that being said, I'm curious to know if there are any hardware differences between the different versions? [I do know there are a few different versions of the Xbox 360 console out there, but I really don't know how the different versions stack up compared to the others.]

Anyway, hope this kind of gives you an idea of what's been on my mind here. If anyone happens to need more details or have questions, please be sure to ask & I will be sure to answer back!

:)