First - I use the same film mid-day, morning, evening, and night. It matters more how you use it than what you use.
During mid-day my negs turn out with too much contrast if I expose normally. So I overexpose the film, as in any high contrast situation, and use gentle agitation and shorter development times to get perfect negatives. If I don't do this I lose some shadow detail and end up having to compensate in printing by using softer filtration, something I don't like to do.
I am in Keith's camp - shooting pinhole mid-day works very well. I particularly like to point the camera directly into the sun.