The scene shows considerable parallels in the sense that both groups are, of course, in a search for a meaningful experience to give their lives meaning.
The pilgrims journey to Rome in order to be near the spiritual home of their religion and, in this sense, there are echoes in...
this pilgrimage in the journey to Pamplona that Jake, Bill and Robert make.
Jake is, of course, in search of some form of spiritual succour and self-definition after his war injury which, of course, emasculates him, leaving him unable to consummate his love for Brett Ashley. One might argue that he visits Pamplona, a symbol, via its Fiesta, of passion and the confrontation of death in much the same way that the pilgrims visit Rome to see a site of the veneration of a similar confrontation of death, that of Christ's transcendence of death with his crucifixion and resurrection.
Jake, one might argue, has suffered a form of half-death after his injury and is in search of others who confront and face down death. However, in Robert Cohn we have another man who, in one way demonstrates the bravery to box and face violence but who is powerless and needy in his love, particularly when compared to the bullfighter with whom Lady Ashley later elopes, a true confronter of death as opposed to a man capable of organised and sanitised violence and who confronts the very real prospect of being killed.
Of course, for Jake, as so many of the 'lost generation' that Hemingway depicts - Bill being another, but a counterpoint to Jake, still in possession of his procreative powers - his relationship to religion is a complex one, part of the ongoing 'ontological crisis' of modernist art that Peter Nicholls (in his book Modernisms) depicts as a defining characteristic of modernist art. At one level, we see Jake attracted to the certainty that the pilgrims have in their commitment to a faith that gives their lives meaning but himself, injured and struggling with a love he cannot consummate and a life defined by the horrors he has seen in war, unable to commit the necessary faith needed to gain meaning in life. Thus he, along with Cohn and Bill journey to Pamplona instead of Rome in search of a tangible and life-affirming show of vitality. One might, indeed, argue that in the spilling of blood and the sacrifice of life in the bull-ring we have echoes of the Catholic sacrament of the eucharist.