I like the idea of "primrose" for a name concept, but I think the word is too awkward. Because of the shape of it - the way my mouth moves when I say it is sort of unpleasant. It bothers me. Also the word "prim" in it makes me feel a little cold.
Princess seems like a sweet name given by a smitten dad, and might be a little heavy to carry, but it's okay. It would never occur to me to name a child that, though. Doesn't appeal to me personally.
I like
Precious more than either - although it's not a personal fave either.
- mirfak