Actually, it's not so cut and dried. I don't have a formal reference to hand, but this is discussed in the last chapter of Stumbling on Happiness - I can dig up the reference if required. Basically, what seems to happen is that having kids leads to many really extreme experiences - first steps, first words, as well as the sort of terrible experiences talked about in this article. We tend to remember these extreme experiences, particularly the good ones, much more than washing nappies every day, and that leads people to report a level of happiness that isn't borne out if you get them to record how happy they are at random times on random days where they're much more likely to be washing nappies.
None of which really matters, of course. If you want kids you'll probably love having them, and if you don't you'll probably be happier without them.
Short version: Basically, the evidence is to the contrary. Parents are "more happy."