I've read papers comparing them, but never seen a study that used them together. Is this done? Why or why not? Suppose you use ANCOVA to analyze a reduced sample of matched pairs generated using propensity scores (assuming the propensity scores are estimated from the complete set of confounders X that jointly effect the outcome variable Y and the treatment variable T). Suppose the model has T (considered as a grouping variable for ANCOVA) along with covariate Z predicting the continuous variable Y. Will estimates of the effect size for the treatment and the regression coefficient for Z be biased if Z is included in the set X or if Z and Y are not independent? I would love to find articles that discuss ideas along these lines.
I do no know of a reference that discusses ANCOVA, but the following paper discusses regression modeling applied to matched data:
Ho, Daniel, Kosuke Imai, Gary King, and Elizabeth Stuart. "Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference." Political Analysis 15 (2007): 199-236.
Chapters 9 and (more particularly) 10 of Gelman & Hill also discuss the topic.