As summarized in the article, the big differences are:
The social psychologist in me likes this as an example of the Social Desirability Bias. When speaking directly to another human being, we report greater life satisfaction, we are more critical of politicians, and more sympathetic towards members of minority groups.
The statistician in me thinks this is a good example for discussing sources of error in research. Even a completely conscientious research using valid, reliable measures may have their data effected based on how it is collected. It might be interesting to asks students to generate lists of research topics (say, market research about cereal preference versus opinions about abortion) and whether students think you could get "true" answers via telephone or web surveys. What is a "true" answer, how could we evaluate or measure this? How could we come up with an implicit or behavioral measure of something like satisfaction with family life, then test which survey modality is most congruent with an implicit or behavioral measure? What do students think would happen if you used face-to-face interviews or paper and pencil surveys in a classroom of people completing surveys?