Stylistically, the main similarity between these pieces is that both Pope and Bunyan are giving a nod to the epic tradition. Bunyan's work centers on the character Christian's epic journey to get to the Celestial City and the obstacles he faces on the way; the work is a religious allegory of a Christian life and being saved. The Rape of the Lock employs features of the epic, such as the epic catalogue (in describing Belinda's toilet) and climaxes with a great battle (a card game) and a trip to the underworld (Belinda's swoon/sickness).
A major difference, however, is the tone underlying each work. Bunyan intended his work, as obvious and even hackneyed it might seem to us, to be taken as didactic and completely serious. Readers of The Pilgrim's Progress were supposed to come away from the tale with an idea of how to live a Christian life and subsequently follow its model. The Rape of the Lock, however, was written for a different purpose: to satirize the petty affairs of the upper classes. As a result, readers of the Rape were not supposed to actually believe that the card game between the noblemen is seriously comparable to a battle in war; rather, the extreme exaggeration brings out the frivolity and unimportance of aristocratic intrigue.