It's a bit like asking Burger King v McDonalds, Mac v Apple or in photographic terms Canon v Nikon. For most post processing purposes Aperture and Lightroom are two of the biggest in the market place. I've always been a big Lightroom fan almost since it first appeared. It seems so much more intuitive than Aperture (strange but true for an Apple product, I usually find them easy enough to get round), and of course the extra control it gives you is much more simple to implement with Lightroom than Aperture.
However, recently I have been tinkering with Aperture. There's a certain something to it I like. It's difficult to put my finger on it, maybe it's just because its different, maybe it's simply the fact I really want to use it over Lightroom. I can't quite fathom it out.
Anyway, here's a quick edit in Aperture from an old image I shot a little while ago. I kinda like it. Although it's still back into Photoshop for a final framing, which having seen on a blog post somewhere, I am kind of liking!