It has boiled over on occasion in the past, including a couple of times at Scottrade Center in St. Louis when Keith was playing in the NHL.
"There was a bunch of fights and a bunch of witnesses to those," Brady said. "We were in the locker room for those, and in the wives' room, when my dad was playing. We weren't afraid to fight but we were always playing five minutes after that.
"I got hit from behind once and I think we fought after that. You just take it and fight about it."
At 6-foot-3, 196 pounds, Brady is an inch taller than Matthew (6-2, 202). He doesn't believe he'll be intimidated in any confrontation and said he isn't worried about any reputation preceding his NHL debut.
"I think my family thinks I'm tougher than him and Matthew's not messing with me anymore," Brady said. "If that's a mark, I'll have to deal with it and I'll try to find my game."
Whenever that first NHL game between the brothers takes place, Brady said he thinks he knows what it will look like.
"I don't think it's going to be much different (from growing up)," he said. "I think it's going to be pretty physical. I don't think we're going to take it easy on one another.
"Probably a lot of talking. We're probably going to be chirping back and forth."