When does it pay to break the matches for analysis of a matched-pairs design?

Two methods of analysis are compared to estimate the treatment effect of a comparative study where each treated individual is matched with a single control at the design stage. The usual matched-pairs analysis accounts for the pairing directly in its model, whereas regression adjustment ignores the matching but instead models the pairing using a set of covariates. For a normal linear model, the estimated treatment effect from the matched-pairs analysis (paired t-test) is more efficient. For a Bernoulli logistic model, matched-pairs analysis performs better when the sample size is small, but is inferior to logistic regression for large sample sizes.