For at least a couple of seasons, one or other of them - sometimes both - has looked to be on the way out of Wigan. This front row has never, it seems, been big enough for the two of them.
Of the two, Cowie ranks as the senior troublemaker. At 31, he is also the senior member of the Great Britain squad preparing to meet New Zealand at Huddersfield on Saturday.
"He's a one-cap wonder," says O'Connor [the cap came five years ago against France]. "There were a lot of injuries and I was drafted in - and drafted straight out again," he recalls of that brief taste of Test rugby.
Far from anticipating this as the year of his return, it might well have turned out to be his last in the game. Protracted contract negotiations at Wigan seemed to be getting nowhere, with Cowie's reputation as one of the awkward squad doing him few favours.
But Cowie's early-season form was so good that the club bit the bullet. "They gave me the money I wanted," he says. "Or we compromised."
So his turbulent times at the club go on. Only last year, he was sent home from Wigan's World Club Championship trip to Australia after missing training.
"There were a lot of politics involved," he says. "I was the scapegoat over that."
In general, though, Cowie argues that he has reformed on and off the field. Always a damaging player on his day, he has found more consistency.
"I always found it hard to motivate myself for games against lesser teams," he says. "Especially playing for a side like Wigan, you knew you didn't always have to perform.
"I've mellowed as a person as well," he continues. "There's not as much testosterone these days."
As Cowie's star was rising once more in the first half of this season, O'Connor's was plunging. A first-choice prop on the 1996 tour to Papua New Guinea and New Zealand, he was fourth in the pecking order at his club and virtually ignored for Wembley.
"I probably didn't do myself any favours after that. I wouldn't say I was sulking ['Yes you were,' Cowie interjects], but I wasn't happy."
The Wigan coach, John Monie, has monitored the ebb and flow of both props this season. "Terry didn't have anything to complain about," Monie says. "He wasn't playing well enough to be in the team."
O'Connor admits now that it took him a while to put that behind him and buckle down again. When he did, he became the form prop of the play- off series.
"He's probably worked me out by now," Monie says. "He'll realise that if you put the form on the board, regardless of what has gone before, you'll get in the team.
"The two of them have had seasons that are the reverse of each other. Neil was going great early on and then had problems with injuries; Terry had a double hernia operation and a slow start and is just producing his best now.
"But they are both big men with plenty of aggression. They won't back down and they've plenty of character about them. I wouldn't want to go on a night out with them, but you don't want a club full of milk-drinkers."
If Cowie was the latest of late additions to the squad - his name did not even appear on the prepared list - O'Connor's transformation is summed up by a geographical accident this week.
In the wilderness after Wembley, he played for the reserve side at Hunslet. "He doubled the crowd, because his mum and dad went to see him," says Cowie.
"Now that is what I call finding it hard to motivate yourself. I was back there on Monday training with Great Britain - and there were more people watching," O'Connor says.
With Cowie and Tony Mestrov re-signed for next season, Brett Goldspink recruited from St Helens, Stephen Holgate also used sometimes at prop and Neil Baynes forcing his way through from the Alliance team, it could be harder to get in Wigan's front row than Great Britain's next year.
In fact, it is has been rare for Cowie and O'Connor to be on the field together. "All the props we use give us something slightly different," Monie says. "Cowie gets the ball available - sometimes at the wrong times, but you have to live with that. You wouldn't want him to stop going it.
"O'Connor probably gives you more go-forward, but Cowie, when he's playing well, is the stronger defensive player and Mestrov outworks the both of them. Between the three of them, you've got a lot of different qualities."
The way O'Connor has re-asserted his qualities has changed plans at Wigan. He was the prop destined to leave this winter, to balance the books as much as anything, and the deal to take him to Halifax was virtually signed and sealed.
"Now John has told me he wants me to stay," he says. "I'm just putting it all on hold until after this series.
"I hope Neil and I are in competition for places. I don't look on him as a rival - but I'll be upset if I don't play."Reuse content