Why are propensity scores better than post hoc matching?

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Why are propensity scores better than post hoc matching? Isn’t a propensity score just an aggregate of many matched characteristics? Would we obtain the same results if we used post hoc matching across 10 variables and if we created a propensity score for those 10 variables? Why or why not? Would pairing propensity scores that are not exactly equal be effectively the same as pairing two participants that are matched on 9 of 10 variables?

 

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