It's fascinating to note how markedly different predictions are in a forum from what actual scenario-based comic book history suggests.
Canary actually has what would be considered "round" wins over numerous people in and above current DCnU Superman's class throughout her long history. To name only the first coming to mind, she has bowled over and stunned Silver Age Superman, along with the rest of the pre-crisis JLA, knocked put the powerful Bronze Age Supergirl, dropped pre-flashpoint Supergirl with far less than full power, and literally BLOWN CLEAN OFF the head of an Amazo that was stronger than pre-Flashpoint Superman AND Wonder Woman combined.
Change this thread to a scenario encounter or an auditory (I.e. sound) gauntlet. There's material enough to give Canary her just due against Superman and a number of otherwise improbable others if you avoid a direct conventional affair.