They basically both have an 'ugh fine' relationship according to what Underfella said. So there's a lot of them fighting (not in a violent way) or being sarcastic to each other, minding their own buisiness. Sans and Papyrus try real hard to be the 'mature/cool brother of the two. Also, he actually knows about and remembers SAVE and RESET. Papyrus is shown to be able to block Fell!Undyne's attack. Also he can use orange bones, sharp bones and spiked bones unlike his counterpart, Papyrus's strength, speed and damage causing is incredible comparing with his counterpart. He has the same Abilities as his Undertale counterpart, but Papyrus's summons bone are red. Papyrus is a lot more powerful than his Undertale counterpart. He also 'HMPH''s and 'MWAH HAW HAW HAW!'. He, like Sans, tries to be cool and collect. Papyrus loves evil puns, but he hides this very well. He wears a red cape, a pointed black battle body with a golden symbol on the left, long red gloves, black trousers with a red wrestle mania belt with the phrase 'Bad Boy' on it, and red heels with 3 black stripes. Papyrus is a tall skeleton with semi-closed eyes, has a scar on his right eye and sharp teeth. Sans attempted to attack Asgore in anger for hurting his brother but was stopped by Papyrus, who believed that if Sans could have fought Asgore before he stepped in, then what was his sacrifice for? Asgore declared that an act of defiance would not go unpunished and scraped his fingers across Papyrus's right eye socket, giving him his scar. Papyrus accepted the offer and became a member of the Royal Guard. Impressed by Papyrus's speed and bravery, Asgore offered him a place in the Royal Guard in exchange for Sans' life being spared. But before Asgore could carry out the task, Papyrus selflessly jumped in to save his brother's life. Papyrus was present at the execution where Sans apologized to him. At some point in the past, Asgore was about to execute Sans by crushing his head for unknown reasons.

Pic of underfell papyrus