While praising Giroud's role in France's World Cup triumph in 2018, Benzema was disparaging of the veteran when asked to compare themselves.
The Real ace said it would be like comparing "a F1 with a go-kart".
Former Monaco striker Berbatov wrote for Betfair: "I will not take sides. For me, this is far from the right way to manage things. It can be entertaining for the fans and doing business for the media, but it is disrespectful.
"Both are great players, they have their strengths and weaknesses on the field. They also have their reputation, their ego, they know how good they are, but I don't see why it is important to know who is the best.
"I'm never a fan of this stuff. If someone has a problem, just pick up the phone. I don't see any point in knowing if mine is bigger than yours."