I really like Aperture for everything except the image processing pipeline, in which I think Lightroom's is superior. In my opinion, Lightroom seems to combine (concatenate) operations together from the different sections of the Develop pane, whereas Aperture would appear not to.
This is not a big deal if you are doing small tweaks around an image. However, if you are really shifting contrast, colour balance, etc., you will find that Aperture clips more readily, more often. Moreover, the interpolation between the "curves" (Histogram points), would seem to behave like a cardinal-spline - meaning the closer you move the points, it just compresses the curve - so you may go from a smooth curve, to something quite sharp (the curve is compressed in space by being pushed up and down, with the limits of the curves going beyond the values of the set points). Cardinal-splines are easy to program however, because there is not need to calculate the tangents, which may explain something. To the people who don't understand what the hell I am talking about, when you move your histogram points close together, it will result in the visual equivalent of clipping, or worse, unintended solarisation.
So, with Aperture, I found I couldn't “overwork” the dials as much as you can in Lightroom. Aperture seems to have very safe limits, even when you ignore the sliders and type numbers up to their highest value. I do think Aperture has a more “pure” approach to image processing… and the new RAW 2.0 conversions are very nice. But I think Lightroom handles shadows more delicately (it won’t crunch them as suddenly); plus it has curves controls, which I find handy and intuitive.
The other thing that bugs me both in Aperture and Lightroom is that you cannot reorder the modules, so that the processing happens in a different sequence. However, in Lightroom, this limitation seems to be somehow less apparent, or maybe I need to get used to the tools… In Aperture, if I wanted to go the full monty in Highlights & Shadows, for example, I would prefer that it did this as part of the Levels adjustment (which is pretty much your last chance to change the overall shadows and highlights, contrast, etc). As it stands, the highlight/shadow controls come after Levels, and inherit whatever you may have done to the image (clipping highlights, for example), but the highlight control cannot regain what has been clipped -- even though it was there before. (I know you can do Highlight Recovery earlier, in the Exposure module, but I am talking about manipulating the shoulder and toe of the curves [aka Histogram] here more than "recovery"). In Lightroom the Curves and Shadow/Highlight controls are combined into the one module. In this way, Aperture is odd, but it doesn't have to be, as Apple do it "correctly" in other apps.
I have read online that Aperture works in float (generally defined as 32bit or higher), although the user manual seems to have no reference to this. If true, a float pipeline would mean you couldn’t end up clipping an image in the whites or blacks – information would be preserved module to module, so if you did two contradictory adjustments (say, brighten in one module and darken in the next), the detail in the image would not be adversely affected - it would be passed on to the next module (even if you can't see it visually). In most Apple products, this means 32-bit float, and they have it implemented (and documented) in Core Image, Motion, and Shake.
You don’t get far into the processing chain to see that Aperture is not working in float, at least module to module. If you crank the contrast up in the Enhance module, but try to pull the highlights down using the quarter tone controls in the Levels module, you will see that your image has been clipped. In fact, I would say that one would be best off not to touch a lot of the controls in the Exposure and Enhance modules, and try and get it all done in Levels, so that you are not losing too much detail in your image.
I'm not suggesting that Lightroom is any better in the image-bit-depth respect, it just seems to hide it all better.
Of course, Aperture does a lot of other stuff quite well. I much prefer the interface, and the organisation side of Aperture. It is more intuitive, integrated, and I find it much faster when it comes to finding what I want.
The difference between Lightroom and Aperture (or C1, Bibble, et al.) is becoming the modern equivalent of shooting Kodak or Fuji. Perhaps the best way to look at it is settle on the one that works best for you. Horses for courses.
I'm sorry to take up so much space in this discussion - I've been thinking about this a bit!