It's better to play ICO first, though not crucial. Since it was released first, Shadow refers back to it, subtly, but ICO is stand-alone. Also it's easier to get used to ICO's unusual control scheme (using Triangle as the jump button) before moving on to Shadow, which has the same plus a manual grip button. (Then again, I think you can customise the controls now...)
RocketJess, blasting off again! http://rocketjess.deviantart.com/art/ICO-Cosplay-You-Were-There-195335164
Play Ico first and Agro gets a nice "Ico" I marking instead of his white diamond marking. Looks a lot better in my opinion, but other than that it probably doesn't matter too much which game you play first, though I agree with others saying it'll help you get used to the control scheme.
I don't really think it'll make that much of a difference either way. I could see wanting to go Ico THEN SotC as that's the order the games were made in and you can see a little bit of a technical progression that way. Plus SotC is, in my opinion, the more fun and exciting game.
However, if my assumptions about the story are correct, then the events of Shadow most likely take place hundreds, if not thousands of years before those of Ico (don't worry, that's not really a spoiler). There is a connection between the two, but not what I would call a direct connection. I myself happened to play Shadow before Ico back in the ps2 days and I wouldn't think anything was lost or gained by doing so.
Bottom line, they're both fantastic games and I think you'll love them no matter how you play them. Enjoy :)
3DS friend code: 2105-8647-3789 Xbox Live and PSN- Judge Judd