Section 6.3 of King, Murray, Salomon, and Tandon (2002). We measured visual acuity using the Snellen ``tumbling E'' eye chart test and compared it to raw survey self-assessments. The Snellen test ranked the Slovakians as having substantially better eyesight than the Chinese, but the raw self-assessments indicated exactly the reverse. We then applied our anchoring vignette correction and drew the same conclusion as the Snellen test. In this situation, we'd still probably prefer the Snellen test to be used rather than the anchoring vignettes, but it is substantially more expensive to administer (especially when done with proper quality controls) and still error prone. That would seem to provide a clear role for the vignettes.
Section 6.2 of the same paper is on political efficacy (how much say do you have in getting the government to address issues that interest you?) in China and Mexico. There's no direct physical test of political efficacy, but the correct ranking of the two countries could hardly be more obvious from well known external evidence; there too, the self-assessments get the ranking of the countries wrong, but the vignette correction gets it right. For measuring political efficacy for other countries and to study variation within these countries, no feasible measurement strategy exists other than surveys, and the evidence here too indicates that anchoring vignettes improve the self-assessments.