The pair briefly played together for the Blades in Bruce’s first coaching job at Bramall Lane as player-manager back in 1998-9.
Twenty years later both are established managers, encamped either side of the footballing divide in Sheffield.
Bruce has only been in the Wednesday job for a month, but has been impressed by Wilder, who has transformed United from an average League One side into a team pushing for promotion to the Premier League.
“Before I came here you have to take your hat off to Chris and what he has done,” said Bruce, who played 11 games for United before hanging up his boots in 1998. “From getting them out of League One to where they finished last year, playing in a certain way in a certain style.
“You have to be complimentary about them. I have huge respect for Chris, but it’s our job – my job – to try and beat them. They have been very good over the last couple of years, and a lot of that’s down to the management.
“Look at what Chris has achieved with lower clubs he has been at, he has done very well. He is a very capable manager and a good person too.
“I had him as a player a long, long time ago at Sheffield United. When you have had somebody as a player you watch them.
“I don’t think I was there long enough to get to know him.
“But certainly over the last few years he has been outstanding in his work. He’s very good.”
United sit second in the Championship with 12 games remaining. But a seven-game unbeaten run under Bruce has seen the Owls narrow the gap on the top six to six points, raising the unlikely prospect of gatecrashing the play-offs.
It means there will be far more than city pride at stake when the rivals meet at Hillsborough on Monday night in a televised showdown. “They are genuine contenders, absolutely,” insisted Bruce.
“With 12 games to go, sitting second in the league, you are a contender.
“But I am not really interested in how well they are doing, it’s what we achieve. We know it will be a tough game, but make no mistake, it will be a tough game for them too.
“In derbies form goes out of the window. It’s on the night who handles the occasion the best, who doesn’t make the mistake.
“Is the derby game won by a flash of genius or a mistake? Let’s look forward to it. The whole country will be watching Sheffield on Monday night, let’s make it a spectacle. Yes, there is always going to be huge rivalry, but let the best team win.”
Since leaving United after just one season in charge – finishing eighth and missing out on promotion to the Premier League – Bruce has gone on to manage Huddersfield Town, Birmingham City, Wigan Athletic, Sunderland, Hull City and Aston Villa.
But the former Manchester United defender expects to be on the receiving end of some good-natured banter from Blades supporters on Monday.
“I think I have had stick all my life,” he smiled. “That never changes. I am sure they will have something up their sleeves, it won’t be very complimentary.”