Experiments versus quasi-experiments: do they yield the same answer?

Life would be ever so much easier if quasi-experiments yielded just as good causal inferences as randomized experiments. Of course, the term "quasi-experiment" covers a multitude of designs. Here it refers to the workhorse of the quasi-experimental design literature: the nonequivalent control group design that includes a treatment group, a control group not receiving treatment, and a posttest for both, but where the assignment of subjects to conditions is not controlled by the researcher, and is certainly not random.