I'm not sure why Gingrich is considered a masterful political operator. Ok, so the Republicans won back the House in 1994 after forty years. But I don't see why it would have been particularly difficult for another GOPer to do that, especially given the cack-handed performance of the early Clinton administration. I mean, the 1994 Republican Revolution was basically Gingrich's only success. Following that, he helped instigate a government shutdown which severely weakened the standing of the Republican party with the American public, whilst simultaneously boosting Clinton's credibility with them. Following that, he embarked upon a disastrous effort to impeach the President which spectacularly backfired upon the GOP, leading to them actually losing House seats in an election that should have seen them fatten their majority. He was also the target of an attempted coup by his own party members, and following the 1998 election he was effectively booted out of the office of Speaker, again by his own party. Basically, he achieved success in 1994, only for it to turn to dust within the next four years, largely as a consequence of his overreaching himself.
By contrast, whilst Boehner is hardly a master strategist, at least he hasn't managed to single-handedly boost the credibility of the incumbent President (that was largely the work of members of his caucus), and hasn't been booted out of the speakership by his own party.
Yeah, basically this. It shouldn't even be a contest between the two.