What's surprising?
No matter what differences you perceive (and I can't see any terribly significant ones) you've got to remember that especially when you're looking at JPEG images, you're not just seeing what your camera and lens can do. You're also seeing the results of the particular camera's JPEG compression algorithms, in-camera sharpening and processing, etc.
In particular, in these two images, it looks as if the Digilux 2 is preset to apply more unsharp masking to the image than the R-D 1. This can yield sharper-looking images... under some conditions. Under other conditions, this artificial sharpening can increase image noise and lead to an over-processed look. (It also plays havoc with noise artifacts, making them much more exaggerated. That's one reason why fixed-lens compacts such as the Digilux 2 are usually limited to an ISO rating of 400, while the R-D 1 goes up to 1600.)
Besides, what's the point, really, in comparing these two cameras side-by-side? You use them very differently for making pictures. The Digilux has a built-in zoom lens and a lot of automation features, which make it very convenient when you want to carry one camera that can do a lot of things. However, you also give up some things, such as lens interchangeability and an optical viewfinder. The R-D 1, on the other hand, has less automation and doesn't pack as many features into the same package -- but it has an optical range/viewfinder that lets you see the subltest nuances of the subject (rather than the pixels of an EVF) and can use just about any M-mount or 39mm screwmount lens from the 1930s to today.
In a way, your test proved that they can provide very comparable results under conditions that suit them both. That should be good news -- it means you can use whichever one has the features you want for the type of picture-taking you want to do, with confidence of getting good-quality images.