Backstory

Judas Betrays Jesus

Judas Iscariot, one of the 12 disciples, makes a deal with the authorities to turn identify and turn over Jesus in exchange for money.[1]

Peter Denies Jesus

Peter, also one of the 12 disciples, denies that he knows Christ three times the night that Jesus is taken by the authorities.[2]

Rationale

Depending on how you look at it, denying your friendship with a person can be a betrayal, but I think actions boil down to two factors: motivation and consequence.

Judas' motivation for betraying Jesus isn't explicitly given in the text. Some believe it was solely out of greed to get the 30 pieces of silver; others believe it was to "force" Jesus in to taking over the kingdom—remember many thought the Messiah would overthrow Rome and restore Israel to its David-era glory. Because there was money exchanged, I believe his motivation was greed (the love of money is the root of all evil!). Judas was ready to jeopardize his friendship with Jesus, the freedom of the disciples, Jesus' life, and all they had worked for, for a handful of silver. That is the spirit of covetousness. When we stop caring what happens to those around us just because something seemingly benefits us, we're crossing a dangerous line. A large-scale, modern example of this is covered in The Devil We Know, a documentary about DuPont sabotaging the water supply around the world in order to continue profiting from Teflon.

Then when Judas, who had betrayed Him, saw that He had been condemned, he felt remorse and returned the thirty pieces of silver to the chief priests and elders,
Matthew 27:3 NASB

Peter's motivation was likely fear. I imagine Rome had a "guilty by association" type of system, as many modern countries still operate this way. For instance, if you're at a party where drugs are present, you can be arrested too. If you have knowledge of a crime and don't report it, you're considered an accessory. By modern definition, the disciples would have been considered accessories to Jesus' "crime" and likely would have been arrested too. After Jesus was taken and made it clear that He wasn't gong to put up a fight, Peter and the rest of the disciples went into survival mode. In Peter's case, he sought to put distance between himself and Jesus to avoid the same fate. The most modern example I have of this (where it's not just in jest) occurred in my family during my grandfather's era (so early 1900s). There was a portion of my family that was born light enough to pass for white and some of them chose to do so to reap the benefits of being white in the Jim Crow era. In order to do so, they had to deny everyone in the family who could not or would not pass.

Of course neither of these motivations are good, but Peter was forced into survival mode by a situation he had no control over. Judas created the situation. I feel that Judas was more deliberate in his action; he thought it out enough to approach the authorities, make the deal, and actually carry out the plan. Judas' actions were premeditated.

56 But a certain maid beheld him as he sat by the fire, and earnestly looked upon him, and said, This man was also with him. 57 And he denied him, saying, Woman, I know him not.
Luke 22:56-57 KJV

The second aspect I mentioned was consequence. I had a friend once tell me he'd rather have someone intend to shoot him but miss than to have someone who loved him but accidentally shot him. In this way, we can have harmless intentions but create very harmful situations. The consequence of Judas' betrayal was the death of Christ. The consequence of Peter's denial was...nothing.

Judas' betrayal doesn't just end with Christ being captured, Christ is tortured and murdered. It doesn't end there either, though. In the aftermath of Christ's death, Judas kills himself. Absolutely nothing good comes from his actions (well, minus the fact that we all have enteral salvation now but that was going to happen anyway). On the other hand, Peter eventually repents of his actions, and goes on to become a prominent figure in spreading the gospel.

Ultimately, we make mistakes all the time and in a way, each time we sin we betray or deny God. However, it is our motivation and our willingness to change that ultimately matter. So at the end of the day, I would choose to be a flawed human who learned from my mistakes and caused little harm over a flawed human that let my choices be the death of me and another person.

References and Footnotes

1. Luke 22:1-48
2. Luke 22:54-62
3. I found many versions of "Would You Rather?: Scripture Edition"; this question was found in a version made by Megan of Church Leaders