Some fans have questioned the arrival of the former Brighton & Hove Albion manager, who has signed a two-year deal with the Black Cats.
"Everybody knew what Di Canio was about and there were a few eyebrows raised when he got the job," Byrne told BBC Sussex. "I think Gus is a little bit calmer.
"He wasn't short of controversy when he was at Brighton. When the Luis Suarez affair blew up at Manchester United [with Patrice Evra], he wasn't slow to put his point of view in the national newspapers.
"He is an interesting character and if he does well, they will idolise him and he will be revered."
Poyet begins his new role with Sunderland at the bottom of the Premier League table.