I wouldn't say that exact expression is common, but the construction of "more X than X" is somewhat common in AmE, where X is the same person, quality, or even institution. Usually X is somebody or something well known for a certain quality.
It means that the person or thing at the beginning of the sentence exudes even more of the quality that the person or institution know for that quality has.
So in this case, somebody is better at exhibiting Popish (I guess you capitalize a theoretical proper adjective) qualities (whatever those are perceived to be) than the Pope himself.