The Celtic skipper spent eight years at Easter Road before moving to Glasgow in 2007 and was in the Hibs side that lost to Livingston in the League Cup final nine years ago.
"It'll be hard for us but it'll be hard for them as well," he told the Celtic website. "It's a huge occasion for them. It's been a long time since they won it but we want to get our hands on it as well.
"Every season it seemed to go on an extra year, they still wouldn't win the cup. Hopefully it goes on another extra year for them again.
Brown is confident that the SPL champions will be able to shackle Hibs dangerman, Leigh Griffiths, and is fully aware that Sunday's opponents carry a greater threat than just the on-loan Wolves man.
"We've got great defenders and a good team spirit as well," he added. "We're solid as a team and kept two clean sheets in the last two games so we're hoping to take that into the cup final.
"It's everyone's job, as a team, to look after him - we work together as a team going forward and going back on the park.
"But it's not just about Leigh Griffiths, though. He's a great player and we've seen that this season, he's showed you how good a player he is but there are 10 other players on the park we have to look out for as well.
"It's a huge game and a huge occasion. Everyone in the dressing room is looking forward to it and we've been looking sharp in training.
"The lads have been enjoying their football. The pressure is off and they've been able to go out and show what they can do. It would mean a lot to win the double. It's been a great season so far and we want to keep that going.
"But we know what they're all about and it's 90 minutes, 11 v 11, so it will be interesting. Everyone wants to win everything in our squad and the Scottish Cup is huge for us."