The way it has been explained to me, and the way it is inset into my mind is that 래요 means more like "I intend to" or "I've decided to" and 고 십어요 is more like "I would like to," or "I want to." In that sense, 레요 is a little stronger or more assertive as it indicates intent whereas 십다 indicates desire. (Of course, I'm using first person to illustrate, but the grammar patterns are not first person of themselves).
Of course, if someone wants to critique me on my answer, that's fine, too. The way I hear them used in Korean, I think it fits what my idea is, though.