Firstly, I think both games are really cheap now (as my friend bought Shadow off the PSN store for $5 a few weeks back with a PS+ discount) and I know they come together in a collection, which I do have. I actually just beat Shadow on the PS3 the other day as I got the collection when it came out, I played through ICO and got its platinum, then started playing Shadow but some other game must've came out, interrupted me, and I just got back to playing it recently. The best part was I didn't remember the puzzles in ICO or how to beat most of the Colossi (I remembered the few I did have troubles with when I first played Shadow though) as I did play both on PS2.
In Shadow, you can ride around looking for lizards with white tails to improve your grip and find fruits in trees to up your life. There's just something special about riding around a rather desolate land coming across some life like birds flying around, turtles in a pond, fish in a lake, etc. You kinda explore just to see the sights really and the world is really beautiful as well. But make no mistake, the game is about the 16 boss fights. Just traveling the land even if you just do the Colossus fights and that's it, you become attached to your horse, much like you become attached to Yorda in ICO.
Yes, escort missions do suck but you know that saying "X is the exception that proves the rule"? Well, ICO is the exception that proves the rule that escort missions suck like how Mirror's Edge is the exception that proves 1st-person platforming sucks. You have shadow creatures that try to take Yorda at times, but they are pretty easy to dispatch and not very annoying either. You get a sword maybe halfway through that will 1-hit kill those shadow things as well. Again, the game just subtly, brilliantly, and gradually develops in you an emotional attachment to Yorda (even just through the animations of pulling her along). ICO is mainly about the puzzles, and the puzzles feel really organic and not very "game-y" as you can really work through them most of the time by just looking over the environment and thinking to yourself what would you do if you were actually there. Most of the time when you do get hung up, it's because you're over-thinking it or thinking to yourself "what the heck does this flipping game want me to do?" instead just keeping it simple.
What is actually really awesome about both games after playing pretty much this whole generation of games is that both games actually have real platforming, not this auto-platforming bullshit where you hit X and the game basically jumps for you. It's great playing a game that actually trusts the player to make a fucking jump (which is probably first thing many of us ever did in a game). I noticed this as I just picked up playing Shadow again after I just beat inFamous 2 whose platforming system I really hated as it felt like I was fighting with it the whole game.
Both games aren't just about the gameplay but the overall experience as well. I really think every gamer should at least try these games as they are very unique and different. They might not be for you, but if they are for you, then you'll just love the shit out of them.