Hello Techguy,
I have been going through an eval of both of these products for about the last two weeks. I have used both of them extensively, and they both have their merits and weaknesses, although I haven't written them down anywhere. LR does cost more, $299US, against the $199US for Aperture.
I have found that LR offers a wee bit more, but the biggest thing was color management, and I located this on the Apple web site in one of the FAQ's.
Aperture supports the RGB color mode, not CMYK, Multichannel, or other. Some unsupported formats will cause Aperture to display an "Unsupported Format" message where the image would normally appear. Lab Color and Multichannel can both cause this (depending on whether you're using TIFF or PSD).
I have also seen many complaints in the Aperture forum about corruption within the Aperture library, but I don't know how wide spread that is.
LR is currently shipping version 1.4.1 and Aperture is at 2.1. Adobe has LR version 2 out for beta testing, but I haven't downloaded that to test yet. I did watch the videos about LR v2 on lynda.com, and there are some major improvements.
Adobe touts the integration with their Bridge product and with Photoshop. I don't have Photoshop yet, so I can't comment there, other than what I have seen on lynda.com. Aperture also has PS integration. They both pass a file to PS to be worked on and the saved work is then given back to the other program.
The Bridge intergration just doesn't do much for me at this point, so I am evaluating the merits of the programs themselves. So far, and I will decide in another week or so, Lightroom is the winner for what I want to do. Both are available for a 30-day trial download. I would encourage you to use both and make your own decision. Your mileage may vary, and contents may settle during shipping, but for me, as I said, LR appears to be what I will be using.
I am running on an iMac 24" 2.4G with 4GB of memory, so I have no issues with speed. Note: I noticed that there are already a few replies to this while I was doing mine.