Capitol white is a slightly lighter "version" of the Ivory White. I definitely prefer the CW in high natural light conditions, when it is creamier. A west-facing room is not going to have those conditions, and especially a bedroom, which is used primarily at night and therefore mostly with artifical light. With the sun rising in the east, in the morning, presumably the room is fairly "dark" as well. So bascially, it sounds like for what it is, the room and the times it is more frequently used, is a low-light room.

If you want white walls in such a room, I think you are smart to go with a warm white like CW or IW.

What I would do, if I were you, is get a pint sample of each and paint LARGE swatches on every wall, right up against wall trim and behind furniture. Then, at the times of day when the room is most frequently used, i.e.: mornings and evenings/nighttime, go in there and make a frame with your hands, framing ONLY the paint color (do one at a time) and the trim or piece of furniture. Block everything else out in the frame so that when you look through the frame, ALL you see is the paint color and the trim or edge of the piece of furniture. Do that with both colors, one at a time. That gives you a very good idea of hat each color will look like once it is in the entire room because there is no interference from the current wall color, the ceiling, floor, the other swatch...

That will give you your answer, I think.