Liners with chamois can work well with the right shorts over them. It all comes down to the seam pattern, in my opinion. If the seams are in the wrong places, in either the liner or the overshorts, you can still have chafing. After having used normal street shorts over underwear-type liners with chamois designed for cycling, I've switched to "normal" looking shorts that are designed for cycling, but still use separate liners or spandex bike shorts under them. The cycling-oriented designs usually have materials and seam patterns that provide more durability and flexibility with less chafing.

tsl makes good points about moisture. Longer rides with two layers are less comfortable than with a single layer bike short. I always wear spandex cycling shorts (no extra layer) for anything over a few miles in warm weather.