Regardless of any intended or unintended similarities, "Brave" had a sales increase of 80% over the past week, according to Nielsen BDS, which may be in thanks to its proximity to Perry.
Many Twitterers, Tumblrs and other outlets put the songs side-by-side -- which you can hear below -- as "Roar" leaked over the weekend of Aug. 9-11 and the song went on sale on the 12th. Dr. Luke co-wrote "Roar" and claims it was written and recorded before Bareilles' track.
"Brave" made it to No. 61 on the Hot 100 when it first hit the chart in the spring, and rebounded over the sales week that ended Aug. 11 up to No. 66 then to No. 41 this week, selling 51,000 digital copies this week, up from 28,000 the previous, according to Yahoo's Chart Watch.
"Brave" was co-written by fun.'s Jack Antonoff and is the first single from Bareilles' "The Blessed Unrest," out in July. "Roar" is the first single from Perry's new album "Prism": it's at No. 2 on the Hot 100 this week.