What is a classic or particular illustrative example of the difference between consequentialism and deontological ethics?
Many forms of classical deontological ethics have rules like "don't lie" or "don't murder" as absolutes. A while ago, I saw a book by a Catholic writer that argued that when hiding people wanted by Nazis if one was asked directly by a Nazi if one was hiding someone the ethical thing would be to say yes. A consequentialist will look at that and disagree quite strongly. In practice many deontological systems won't go that far and will label some deontological constraints at different priority levels, so most Catholic theologians would as ...
This was demonstrated, in a certain limited way, in Peterson (2009). See also Lowry & Peterson (2011).
The Peterson result provides an "asymmetry argument" in favor of consequentialism:
Another argument in favor of consequentialism has to do with the causes of different types of moral judgments: see Are Deontological Moral Judgments Rationalizations?
Update: see Carl's criticism.