Juve reached their first final since 2003 two seasons ago but their quest for a third title came up short as Barca eased to a 3-1 win in Berlin.
The two sides have not met in the competition since but will battle over two legs in the last eight in the coming weeks.
Bonucci feels Juve - who sit atop of Serie A - have gotten stronger since, while Barca may not have the quality they had in Luis Enrique's first season in charge.
"I never watched back the final from 2015," Bonucci told La Stampa ahead of the first leg of the quarter-final on Tuesday.
"It will be a different game this time around, because our defence has become even stronger. And Barcelona are perhaps not as strong as in 2015, even if they are still a great team.
"We have maybe lost a bit of physical strength in midfield compared to 2015 with the departure of Arturo Vidal and Paul Pogba, but we have more quality. And we have matured a lot since then.
"For Barcelona, Neymar has really made a step up, Javier Mascherano has gotten two years older in defence and Ivan Rakitic has matured in midfield.
"We both have a great defence, but I think ours is better, even if we both play differently."