Slight background on me to show where my perspective is coming from:
I've been into photography for about 4 years now and have been shooting with a Canon 20D since October 2004. I'm (hopefully) budding into getting into professional photography and have done a CD cover shoot for a gospel choir at my university, a campus fashion magazine shoot, and plenty of stuff for the campus newspaper.
Anyway, I've tried both on my MacBook Pro (2ghz, 2gb RAM)... I've only had Aperture 1.1 for a short while, but I immediately found myself liking it much much more than Lightroom. Lightroom is quite sluggish even on my machine, and I dislike the "modes" that is has as well. Dealing with digital photos, I like to be able to seemlessly go from one thing to the next and not be forced to work in a specific flow. The non-destructive workflow is fantastic, and so many features are intuitive (for me at least) and make working with RAW files (which I use a lot of) very straight forward. I can do preliminary edits in Aperture and move directly into Photoshop. All in all, Aperture is more of a pleasure to work in than Lightroom and the interface isn't nearly as crowded.