It is surprising that two top drawer saints have to share a feast day instead of having one each. In fact St Paul does get his own day, January 25th, but it is dedicated to his conversion alone and not to the rest of his ministry or his writings. St Peter does not.
Saint Peter, also known as Simon or Cephas, was one of the twelve apostles. He appears repeatedly and prominently in the gospels and the Acts of the Apostles, usually in a leadership role.
Roman Catholic tradition regards Peter as the first bishop of Rome - or Pope - and subsequent Popes as the successor to Saint Peter. Based on contemporary historical data, Peter's papacy is estimated to have spanned from AD 30 to his death, which would make him the longest serving Pope of all time, at some 34 years.
Early Church tradition says that Peter died by crucifixion under Emperor Nero at the time of the Great Fire of Rome in 64AD, for which the emperor was happy to blame the Christians. The crucifixion took place at Vatican Hill, and he was buried where the Basilica of Saint Peter was later built, directly beneath the high altar. There is also a tradition that he was crucified head down.
St Paul had a very different story. As a devout Jew, he set out to discredit and then persecute the early church, and was on his way to Damascus on one such mission when he was stopped in his tracks by a bright light and heard the voice of God, “Why are you persecuting me?” From that moment on he became a passionate follower of Jesus, in two ways.
Firstly he travelled extensively, spreading the teachings of Jesus throughout the Eastern Mediterranean. He preached the gospel and founded several Christian communities in Asia Minor and Europe from the mid-40s to the mid-50s AD, as detailed in the latter half of the Acts of the Apostles. Secondly he wrote extensively, mainly to the churches he had founded, and often to resolve disputes of theology or church order. 14 of the 27 books in the New Testament have traditionally been attributed to St Paul, though there is doubt about some 7 of these.
In 57AD, he arrived in Jerusalem where he was accused of defiling the Jewish temple by allowing Gentiles to enter, and was dragged out by an angry mob. He was taken to Caesarea, where he was held for two years until a new Roman governor suggested he be taken back to Jerusalem to stand trial. Paul then exercised his right as a Roman citizen to appeal to Caesar and set sail for Rome. He arrived in Rome c 60 AD, and spent another two years, often preaching the gospel. His death is also believed to have occurred around the time of the Great Fire of Rome in 64AD.
So why do they share a feast day? One tradition states that Peter and Paul were martyred "at the same time", Peter being crucified while Paul was beheaded. This feast day celebrates their joint martyrdom in Rome, the date selected being the anniversary probably of their death. Perhaps not surprisingly SS Peter and Paul are today the patron saints of Rome.
The picture above combines a portrait of Saint Peter from the Basilica of Saint Paul outside the Walls, Rome (Public domain, via Wikimedia Commons) and a fresco of St Paul, dating back to the 4th Century AD, from the Catacomb of Saint Thekla - the oldest one known of in a Roman catacomb (as reported By Nick Pisa in The Telegraph,28 June 2009 - see https://www.telegraph.co.uk/news/worldnews/europe/vaticancityandholysee/5675461/Oldest-image-of-St-Paul-discovered.html)