It is only in recent years that the battle between these two teams has spilled over into new territory - the British & Irish Cup.
This will be the third consecutive year in which Leinster 'A' and Munster 'A' will have faced each other in the knockout stages of the cross-border competition.
Two years ago Munster 'A' got the better of Leinster 'A' in a semi-final at the RDS that went to extra-time.
Last season, Leinster'A' played away to Munster 'A' a the semi-final stage and won 17-15 in a tight game at Garryowen FC. On both occasions, the winning team went on to win the British & Irish Cup.
While it may be a tougher quarter-final tie than either team would have wanted, Leinster Academy manager and head coach of the 'A' side, Girvan Dempsey, is looking forward to an exciting encounter in early April.
"It's a really exciting quarter-final. There's good history between ourselves and Munster right through the age-grade rugby to the professional game, particularly in the British & Irish Cup over the last couple of years," he said.
Dempsey believes though that whatever the draw may have been for the quarter-final, the reigning champions were always going to end up with a difficult fixture.
"Looking at the pools, I don't think there's any easy tie. Having seen all the teams and their records throughout the pool stages I think the qualification has been pretty tough and in the last-eight there's a lot of strong teams."
The changes to this season's draw for the knockout stages mean that if Leinster 'A' do get past their Munster counterparts, they will be away to either Cornish Pirates or Pontypridd in the last-four - despite qualifying from their pool as the tournament's top seeds.
Cornish Pirates are one of only four sides to have won the British & Irish Cup since the competition began in the 2009/10 season, and they currently sit sixth in the English Championship table just seven points off a promotion play-off spot.
Pontypridd are at the top of the Welsh Premiership table, with a game in hand over their nearest rivals Llandovery.
"It's a tough draw potentially in the semi-final having to go away, and particularly to the winners of Cornish Pirates and Pontypridd," added the former Leinster and Ireland full-back.
"We've experience of both those places over the last few years. Cornwall is a very tough place to play and they've had good success in the British & Irish Cup in the last few years.
"Similarly, Pontypridd are a side who've always been very strong in the Welsh league and have had good success in the British & Irish Cup, and beat us when we were over there last year."
Preparing for British & Irish Cup games can be a tricky task. Video footage of opposition teams is limited and the Academy players are usually preoccupied with helping the province's senior squad prepare for games during Heineken Cup weeks.
"The preparation is challenging because you've obviously limited access to footage, you don't get to see a lot of the opposition that you're playing and then within that you're just trying to prepare the guys in the small amount of time that you have with them," explained Dempsey.
"Our window of opportunity to work together as a team is limited but you just make sure that the information you give the players is pretty succinct and you don't go in with a massive game-plan. You keep it pretty tight and you work on the basics. It's stood us in good stead so far.
"The match against Munster 'A' will be exciting. We had them in the semi-final two years ago and obviously again in the semi-final last year.
"They managed to get the better of us two years ago and we managed to get on the right side of the result last year. This year's quarter-final will be a great opportunity to go head-to-head against a strong Munster side."