Well, I know for a fact that they don't actually improve your eyesight.
It was actually a rumor started by British intelligence during WWII to hide the fact that they had radar technology to detect Nazi aircraft. They created a rumor to explain why more Nazi bombers were being shot down; the RAF pilots were eating carrots to improve their eyesight!
where did you hear that its healthier to eat them cooked over raw? I've always hear the opposite. Carrots are great for your eyes and give your skin a "tanned" glow if you eat enough. But don't eat too much or you will be orange! haha