Brown et al. give a formal treatment of the subject with simulations showing actual coverage probabilities for the various methods. It is worth a read if you want to really dive into the subject.
ref: Brown, Lawrence D.; Cai, T. Tony; DasGupta, Anirban (2001). "Interval Estimation for a Binomial Proportion". Statistical Science 16 (2): 101–133
It looks like Clopper-Pearson is the only method guaranteed to not underestimate the size of the confidence interval (which makes sense, given its derivation), but it almost always overestimate its (unless your confidence interval exactly matches the discrete p-values allowed by the binomial distribution).