At the time of the lightroom beta and Aperture 1.5 I chose aperture because it was ahead of lightroom at the time. However lightroom is catching up (or caught up) with featheres of aperture. Both have the main feature I like...Variations, saves so much HD room on a little change. The only thing aperture doesn't have that lighroom does is curves manipulation. Apple tries to keep it simple and leaves you with sliders and a histogram. While the histogram is ok because theres a slider for quarter and three-quarter tones which helps some. Any color critical jobs get imported into PS and then the .psd or DNG's are saved with aperture. (haven't tried the .dng import yet)
I also prefer apertures way of sorting and archiving projects.
Also I dont know if lightroom has a backup built in but I love apertures vault feature. I also love the way you can store projects offline and keep a referenced .jpg of them for viewing. I store old projects on CD's labeled 001,002,003 etc.. in a folder so I can instantly find any project if its needed later on. VERY handy if you handle hundreds/thousands of client photos ( I don't lol).
In a nutshell you they both essentially do the same thing, I bought aperture with a student discount of $150. Lightroom might have more integration with the CS suite however my workflow works out just great. (aperture still holds the .psd and can edit in an external editor like PS)
Using both, I have chosen Lightroom. Even since 1.1, I've used it...it's at 1.3 now, and has a few more features...
But the biggest thing for me is it's more intuitive and easier to use. I find it's a much faster workflow.
Aperture is easier to tag photos with keywords and meta tags and whatnot, as well as organize the photos...but Lightroom lets you manipulate the photo much simpler. Also, I can't figure out the straighten tool in Aperture...it never works how I think it's going to.
I can't say Aperture is bad...but I like Lightroom a lot, and it's a shame Aperture isn't better...because it was like 3 times the price...
Oh, and adam said he didn't know about built in backup....well Lightroom DOES have a built in backup...in case that's an important feature for you.
One thing that helps a lot is that it's integrated right in with CS3 so it's real easy to just right click and go to "edit with photoshop CS3" and you're right there...and then when you push "save" in photoshop, it adds that copy to your lightroom album stacked with the original.
I've got both, I'm trying the demo of Lightroom and I am borrowing a copy of Aperture. I wanted to like Aperture more but I'm just not. For me the interface of LR is much more straight forward. Aperture is really slow as well. I've got a nice fast mbp and it's still slow! Which sucks cause I'm gonna end up shelling out 100$ for LR when I already have a free copy of Aperture.