The former Colts coach and retired Patriots safety both were part of the network's Super Bowl coverage last season.
They demonstrated on a conference call Wednesday they could be opinionated and feisty.
After Dungy mildly chided Peyton Manning for recent comments in which he expressed concern about the retirements of two veteran Colts assistants, Harrison described it as a "sense of panic" and insisted his former quarterback, Tom Brady, never would have expressed such sentiments publicly.
Dungy's boldest comments were directed at new Bears quarterback Jay Cutler, saying, "We'll see about the maturity level; that's what I would question."
NBC Sports chairman Dick Ebersol said the Sunday studio show will make a big change in philosophy, de-emphasizing highlights and reviews of earlier games in favor of previewing that night's game.
Ebersol said Tiki Barber would continue in his role outside the studio, reporting from the site of a big game every week. - NEIL BEST