We have had good luck with both once we got the hang of putting them on (not being afraid of putting them on too tight and checking the leg openings each time). That said, I bought some used Happy Heinys and they have been blowing out--I think the elastic has stretched just enough that they don't cinch down as well for my 3 month old. Once she gets a bit bigger I don't think this will be a problem any longer.
I also really like Nikky covers with gauze flats folded up. Very absorbent for pees, but messy for poops. They also fit well in gDiapers which fit my daughter very well.
For me it was about trial and error--and I was lucky enough to get in on a set of newborn sized diapers that get passed around to friends as they need them..... included Bummis, Bumpy and Nikky covers, prefolds and gauze flats and Kissaluvs size 0 fitteds. The Kissaluvs are great for poops b/c they don't blow out.