The use of model-based propensity scores as matching tools opens the way to the indirect estimation of mode-related measurement effects and selection effects in web surveys, including a component of selection that cannot be traced back to observable characteristics. By matching and comparing respondents from real independent surveys that use the same questionnaire, but different administration modes, it becomes possible to isolate the selection effect induced by unobservable (or unobserved) respondent characteristics. This study applies a stratification matching algorithm to compare a web survey from a proprietary panel with a computer-assisted telephone survey based on random digit-dialing. The experiment is run in two countries (UK and Italy) to check for consistencies across different cultures and different internet penetration rates. The application to the elicitation of support for healthy eating policies indicates large and significant measurement and selection effects. After controlling for differences in the observed characteristics of respondents and the intensity of internet use, findings suggest that web surveys record lower support and higher neutrality. Similarly, after controlling for administration mode and observed respondent characteristics, internet users are less likely to state support compared to non-users. This suggests that unobserved characteristics play a major role, and post-stratification weighting is not a sufficient countermeasure. As demonstrated by the cross-country comparison, rising internet penetration rates are not a guarantee against this type of error, as disparities in these unobserved characteristics are likely to increase at the same time.