However, having won three of his seven meetings with Celtic and Rangers since joining Hearts at the start of 2020, Boyce is relishing the prospect of going to Celtic Park on Thursday for a match in which Hearts have the incentive of knowing a win will lift them above their hosts and up to second place.
He said: "When I was at Ross County, Celtic were formidable. They were pretty much winning every cup so we would set up defensively because we worried about the quality they had.
"There was one game against Rangers that sticks in my mind when we were 1-0 up at Ibrox and Lee Wallace scored towards the end (Rangers won 2-1 in February 2017).
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"When you set up defensively, you're just delaying their chances to the end. With the quality these teams have, they're going to take their chance so it's a breath of fresh air for me up front to be going into games like this believing we can get something from the game instead of worrying about the opposition."
Hearts drew 1-1 with Rangers on their last visit to Glasgow in October and Boyce felt the way they played that day proves they should not be fazed by either of the big two.
He said: "With the quality we have in our side, we believe we can hurt any team in the league. The Rangers match showed that to me even more.
"In the first half we were alright but they took a 1-0 lead. For about 20 minutes of the second half, I would say we were the better team and we should have scored from open play before Halks (Craig Halkett) came up with the equaliser in the 90th minute.
"You take confidence from it when you go through to stadiums like that and control the game for 20-25 minutes."
Hearts have taken four points from their two league meetings with the Glasgow clubs this term, but they were disappointed with the way they played on their last visit to Celtic Park when they lost 3-2 in the Premier Sports Cup in August.
Boyce said: "We beat Celtic in the first game of the season at home and it was a really good performance but when we went there in the cup, in the first half, we couldn't get out our half basically.
"For me personally, I was picking the ball up 30-40 yards from my own goal and having to buy fouls and whatever.
"We know they're a good team but hopefully we can win the ball in more advanced positions to try and take advantage. As a forward, it's more enjoyable when you go and press teams because you can win the ball high up the pitch and you have more people close to you."