FOXBOROUGH — After a couple of much-talked-about skirmishes last week in training camp, Patriots players said it was time to face off against some new faces.

They got that chance Tuesday, as the New Orleans Saints joined them on the fields behind Gillette Stadium for a full-pads practice that drew an overflow crowd, fans excited to see not just their own team but also one of the best squads in the NFC in recent years.

The 14,000-plus on hand weren’t the only ones who were quick to show their admiration: After practice, members of both sides were quick to offer praise to the other side.

Perhaps most effusive was New Orleans interim head coach Joe Vitt.

“This franchise that we’re going against is the Microsoft of our industry, what they’ve done,” Vitt said. “Bill Belichick is the coach of my era. He’s the Don Shula, the Bill Walsh of my era.”

High praise indeed.

“It’s always great when we practice against a class franchise like this franchise,’’ added Vitt. “We got in a lot of good work today.”

Vitt said the Saints’ previous experience of shared practices with New England (in 2010) made things easier this time around.

“I think there’s a lot of trust involved,’’ he said. “We know what we want to get out of each day. The biggest thing is the players trust one another — they know we can work tempo, angles to the ball, without beating each other up. Whenever you have that trust between two teams, I think it makes it a lot more compatible.”

New Saints defensive coordinator Steve Spagnuolo, who was raised in Grafton, got the benefit of having family on hand.

“I think the two organizations — from my standpoint, being new in New Orleans and having grown up with this one, two great organizations getting together, helping each other. And I think the players were terrific too,” he said.

Belichick, who flew with Spagnuolo and Vitt to the funeral service for Garrett Reid, son of Eagles coach Andy Reid, on Saints owner Tom Benson’s private plane earlier in the day, was also quick to compliment New Orleans.

“It’s great to work with the Saints,’’ he said. “They’re a great organization. I have a lot of respect for the ownership, with Mr. Benson and of course [suspended head coach] Sean [Payton] and Joe and his staff and players.

“We had a really good practice out there in terms of working with them and just getting better. [There are] a lot of things we need to improve on. They’re a real good football team, they do a good job.”