Martinez is in his first season Everton boss, Moyes having departed for Manchester United, and they are unbeaten in the Premier League.
Martinez and Pardew go head to head on Monday night, live on Sky.
Asked if Martinez had big shoes to fill, Pardew said: "Yes, but they have signed some good players and you would have to say that they have got what looks like a stronger squad than David had last year.
"Certainly the chairman there has done his bit, and they could be the surprise package of the season."
Martinez lost Marouane Fellaini, who followed Moyes to Old Trafford, but James McCarthy, Gareth Barry and Romelu Lukaku have all arrived.
Everton have beaten Chelsea and West Ham and drawn with Norwich, West Brom and Cardiff, and although they slipped out of the Capital One Cup at the hands of Fulham on Tuesday, they went into the weekend sitting in sixth place in the Premier League.
"Everton's retention of the ball will probably be greater under Roberto," said Pardew. "But what we have shown is that we have got a real offensive look about us. But we have got to make sure we are tight enough to cope with that.
"We weren't against Hull, but in the last three or four games other than that game, we have been and that's important.
"If we are going to have a more offensive look, then we have got to make sure the back door is shut.
"It was on Wednesday night (in the 2-0 Capital One Cup win over Leeds). We got a clean sheet again and that was a good thing.
"Everton have always been a difficult side to beat, especially at Goodison. It's a tough place to go. We got a 2-2 last year and we really had to work hard to get that. They are in good form and it's a tough game to play there."
Everton v Newcastle is live on Monday Night Football, Sky Sports 1HD, 7pm