I have recently switched to Aperture from Lightroom.
Two things Aperture does sinificantly better (IMO) are actual photo storage management, and "lights out" viewing and editing. I like to have all my raw files stored in a central location (Aperture library), and I like not caring about what the software does with the files. When I was using Lightroom, my Pictures folder was a mess - and I had to do my backups to the external drive with Chronosync. Not anymore. Aperture's Vault feature is amazing.
With version 1.5 you can also store files in your own folders, just like with Lightroom... I just don't know why would you want to.
I like the Aperture raw converter resulst to better than Lightroom's (I use an Oly E1).
The thing that Aperture does dramatically worse than Lightroom is dust patching. By default the tool just blurs the area (not very helpful). You can switch the tool into Lightroom-like "stamp" mode. However, unlike Lightroom's implementation, the tool does not always find a good place to stamp from. If your dust spack is on the edge of the photo, the "rubber stamp" may be placed outside the frame. What is worse, patching is excruciatingly slow. If you patch 10-15 spots on an image, the Loupe tool becomdes almost unusable due to lag.