Brown, 22, has become a Scotland regular since the turn of the year and has handled a £4.4million move from Easter Road to Celtic with aplomb.
Collins told the Edinburgh Evening News: "No doubt about it, Scott is one of these players that rise to the occasion.
"But every game is a big game for Scott Brown, I think that's what makes him that little bit different. Nothing fazes him, I think he proved that in his first big game for the national team against Italy away. He shows the opposition no respect, which is what I like about him."
Collins expects Brown will improve by adding more goals to his game but he believes his ability to run at defenders and willingness to track back make him two players in one.
"He has not scored the goals I think he will score in his career," the former Scotland midfielder said. "I think that's the next stage of his development, to score more goals from midfield. But he has great energy, he loves to run with the ball.
"He will run forward but as soon as it breaks down, he is the first player to get back to the edge of his box and put tackles in.
"I have no doubt he will be a big player for Scotland.
"I think he gives us an extra bit of energy in midfield. Some managers and coaches talk about defensive midfielders and attacking midfielders, what you get with Scott Brown is both in one."