Development of propensity scores is simply a matter of predicting likelihood of receiving a pseudo-"treatment" as you would handle imbalanced randomization in a clinical trial. The matter of developing such scores, then, becomes a prediction problem. This question becomes the same, then, as using logistic regression versus other techniques for development of a binary prediction model.
Logistic regression is a maximum likelihood routine for a regular exponential family, that means that the MLEs have nice regularity properties, except in the case of singularity. It takes advantage of the fact that the variance of a binary event is related exactly to its mean, and uses that to get better estimation of the curve (rather than a nonlinear least squares regression using the logit curve estimated using least squares for 0, 1 observations). The logit curve is a smooth, well behaved, and appropriately bounded curve for predicting risk. The logit curve gives approximately very similar inference and predictions to other "S" shaped regression routines like probit regression or some arbitrary made up link function. Logistic regression parameters are easily estimated using default software.