A Mike Chaney have done some analysis and these are his conclusions:
* Bayer sensors have a very significantly reduced resolution when resolving detail comprised of mainly red/blue primaries, such as a red sports car with black pin stripes, a blue sweater with red lettering, red soda can with black lettering, etc. In these cases, resolution of the Bayer sensor is reduced to less than 1/4 of its "image" resolution! Black and white details will show the highest resolving power on a Bayer sensor, while saturated color detail will vary greatly. A Foveon sensor is much more consistent, resolving near the full resolution of the images for every color combination.
* Bayer sensors will produce images that are softer and less detailed due to the "smoothing" needed to eliminate artifacts and color distortions.
* Bayer sensors tend to omit chrominance (color) information when sampling high frequency detail. If you look at a picture of a tree that has many small branches with a brick wall behind it for example, you will see that many of the smaller branches "morph" into the color of the bricks in the background. This is because the branches are not wide enough to cover the multiple pixels needed to derive accurate color information on a Bayer sensor. Full color sensors completely eliminate this problem.
* Bayer sensors tend to produce color moire on high frequency detail like the cuff of the jeans below (more visible in center image). (see link above for images)