They might not see eye to eye on the importance of physicality. The two men disagree profoundly on the need for punctuality. But, as Wilder explained ahead of tomorrow's visit to Carrow Road, his quarrelling with Farke is really a phoney war.
"Yeah, it's alright, it's good," the Sheffield United manager replied when asked about his relationship with the German. "Obviously a couple of bits and pieces have happened but what I will say is that we've always had entertaining games. They've not been dull have they. Really, there's no problem. No issues at all."
The 'bits and pieces' Wilder was referring to trace back to September last year when, already angered by what he perceived as City's deliberate time-wasting en route to a narrow victory at Bramall Lane, he also accused Farke of being disrespectful after reporting late for a pre-match meeting involving himself and the match officials. Four months later, when United avenged that defeat in Norfolk, Wilder sarcastically pointed to his watch during United's post game celebrations.
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"I made a reaction after the first game, I wasn't happy with a few things and I don't keep that to myself," Wilder, whose father in law had been taken ill before the return fixture, said. "The second time, there was some personal stuff on that that not a lot of people knew about at the time and the third one, earlier this season. that was a really tight match."
"But I'm full of respect for Dan and his team," Wilder, who masterminded his second triumph over Farke in August, continued. "People like to pick bits and pieces out of it. But I've got full respect for Dan and his side and hopefully, with how we're doing, they have got the same for us."
United travel south tonight fourth in the Championship table, three points behind second-placed City but boasting a superior goal difference. Attributing his squad's position to their "hard work, attitude and ability", Wilder also acknowledged United's players have become more streetwise; something he attributes to their defeat by Farke's men in September 2017.
"One hundred per cent, when we first came into it and possibly myself, we fell for a few three card tricks if you like," Wilder, whose team had just been promoted from League One, said. "You have to learn and move on.
"In terms of the professionalism, maybe there were a few things that opened our eyes in that game. I'm not saying we will copy other teams but we will learn about seeing things out."
Farke, aged 42, is among a trio of managers appointed by English clubs after cutting their coaching teeth with Borussia Dortmund's under-23 side. David Wagner, who recently parted company with Huddersfield Town, also impressed at the Stadion Rote Erde while his successor, Jan Siewert, previously worked in North Rhine-Westphalia.
"That must be one of the most sought-after jobs in Europe now," Wilder joked. "If you get that, then you're guaranteed a good one over here.
"We have different ways of playing, different philosophies and different ways of going about things. But no, full respect for Dan from me."
Despite their feisty battles on the touchline, Wilder and Farke actually have more in common than either they or their respective employers' fans might care to admit. The most obviously similarity is a commitment to attacking football, with United being instructed to "go all out for a win" despite receiving extensive briefings on the need for concentration against opponents with a reputation for scoring late, decisive goals.
"We've looked at their late goal record for a while," Wilder said. "They commit bodies forward.
"All the teams who have been scored late against, they will be looking at the mistakes their defenders have made. Yes, they flood players forward at the end. But the likes of Bolton and Forest, the two they conceded, one was a real poor bit of defending late on. The other was a swing and a miss.
"We had that at Rotherham a while back. If we had defended better there, we would have won the game and not drawn."
"We are set for a 95 minute game," Wilder added. "I'm not saying it will be. They might be a lot better than us on the day. We might be a lot better than them. But that's what we're ready for. The bets will be on it being a tight game."