I have both.
Using both, I have chosen Lightroom. Even since 1.1, I've used it...it's at 1.3 now, and has a few more features...
But the biggest thing for me is it's more intuitive and easier to use. I find it's a much faster workflow.
Aperture is easier to tag photos with keywords and meta tags and whatnot, as well as organize the photos...but Lightroom lets you manipulate the photo much simpler. Also, I can't figure out the straighten tool in Aperture...it never works how I think it's going to.
I can't say Aperture is bad...but I like Lightroom a lot, and it's a shame Aperture isn't better...because it was like 3 times the price...
Oh, and adam said he didn't know about built in backup....well Lightroom DOES have a built in backup...in case that's an important feature for you.
One thing that helps a lot is that it's integrated right in with CS3 so it's real easy to just right click and go to "edit with photoshop CS3" and you're right there...and then when you push "save" in photoshop, it adds that copy to your lightroom album stacked with the original.