Which came first Paramore or Flyleaf?

Flyleaf came first. They were originally called Passerby and they released 3 EPs under that name, of which the first came out in 2002. Their first album as Flyleaf was a self-titled EP released on October 26, 2004. Paramore's first release was their debut album All We Know Is Falling, which came out on July 26, 2005. They do beat Flyleaf by a few months on having the first full-length album, as Fyleaf's self-titled full-length was not released until October 4, 2005, but it clear that Flyleaf was active and releasing music for years before Paramore was.

Flyleaf also hit the mainstream first, with their 2005 single "I'm So Sick" getting airplay on rock and alternative radio, whereas Paramore did not receive any significant airplay prior to their 2007 hit "Misery Business."