Personally I would prefer
Rosemary.
I do think
Primrose is going to get more common because of "The Hunger Games." In the responses I got from this and two other boards to my questions about the names from Hunger Games,
Primrose was the one that the most people said they might actually consider for a child. The only other Hunger Games name (that's in the first book) that many people said they might really use was
Rue.
It was used some during the flower name fashion of Victorian times, but was never very popular. There were 277 people named
Primrose in the 1930 USA census -- 49 of those were men, by the way, probably because
Primrose is also a Scottish surname and they were being given that as a first name.
Though I am not a personal fan, my personal impression of
Primrose isn't "cutesy" but rather straight-laced and traditionally feminine, probably because of the connotations of "prim." Though if I knew a
Primrose I would rather use Prim than
Rose for the short form, just because it's more distinctive.