One important similarity between the two books lies in their respective treatment of the Church. Both Dante and Chaucer were, as with most people at the time, devout Christians. Yet at the same time they were both strongly critical of the rampant corruption and widespread abuses in the Church. The difference, however, lies in how they treated the problem. Chaucer does so primarily through humor; whereas Dante is much more explicitly moralistic and condemnatory.
Pope Boniface VIII is one of the undisputed villains of Dante's Divine Comedy. Appropriately enough, he has been consigned to hell. Dante despised Boniface because he sought to extend the Church's temporal power at the expense of secular authorities. That he did so on the basis of a forged document, The Donation of Constantine, merely added to the offense. Dante's animosity towards Boniface was also intensely personal; he was forced to leave his beloved Florence on account of a squalid power struggle initiated by the pope.
What's all the more remarkable is that Boniface was actually still alive when Dante wrote the Comedy. Yet when another no-good pontiff, Nicholas III meets Dante on his visit to hell, he thinks that Boniface has arrived instead. Nicholas has been buried upside-down as punishment for the heinous sin of simony (the buying and selling of Church offices). Naturally, he can't see anything with his head buried deep into a rock; but, as with all the damned, he can see into the future, and knows full well what hideous fate will one day befall the wicked Boniface.
Chaucer's knocking of the Church is more gentle, but no less effective for that. He proceeds to highlight the Church's many faults by subtle hints and insinuation. The appearances of the various pilgrims in the General Prologue provide a handy little glimpse into the world of Christendom at that particular time. In other words, unlike Dante, he shows rather than tells.
First, there's the Prioress, who despite being in charge of a convent, appears more concerned with showing off her fashionable clothes and flashy jewelry. Then there's the Monk, who's much more interested in hunting and good living than ministering to troubled souls. The Friar is a greedy hypocrite who lines his pockets with church donations, hates the poor, and loves sucking up to the rich nobility. The ugly, pock-marked Summoner is another hypocrite who exchanges church pardons for a hefty bribe. And the Pardoner is an odious creep of uncertain sexual orientation who cheerfully admits to selling fake relics.