Schmidt was coach of Ireland from 2013 until 2019, leading them to their first win over the All Blacks in 111 years of trying in 2016 and to the quarter-finals of the last World Cup.
He returned to his native New Zealand last year, taking over as attack coach under Ian Foster after the All Blacks lost a home test series to the Irish for the first time.
"It seems it's back to the All Blacks of old really, exceptionally dangerous with ball in hand," Catt, a World Cup winner with England in 2003, said when asked what he expected from New Zealand on Saturday.
"I think Joe's definitely brought a physicality to the breakdown and with their ball carrying. That was something that Joe was massively passionate about with Ireland as well.
"Especially in the wide breakdowns, these guys are big guys and they put a lot of pressure in those areas. So it's making sure that we match them physically while being technically good in the same breath."
Ireland captain Johnny Sexton, who played under Schmidt for the best part of a decade with Leinster and Ireland, said his legacy in the Irish set-up was "massive" and his influence on the All Blacks obvious.
"I see evidence of Joe's coaching through the team," Sexton said on Wednesday.
"Joe's done a great job over the last 12 months, they've made big strides."
New Zealand's players have also lauded Schmidt for his part in reviving the All Blacks after that test series loss to Ireland last year, which almost cost Foster his job.
Richie Mo'unga joked on Thursday, however, that Schmidt's passion for the minutiae of the game made him a man to avoid at times.
"You get caught in the hallways talking code with him and you could be there a fair while. You've got to just turn your head the other way sometimes, try and avoid that," the fly-half said.
"Nah, he's awesome, the different perspective of footy he has. I would say that perspective is real basic, and the things that make a team tick really well.
"He really wants to see the best of his footy players and see them unlock their potential, which I find the coolest thing about him."
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