Moyes' side have an excellent record against City, particularly at home, having lost just one of the last 13 Premier League meetings between the sides at Goodison Park.
Yet Moyes feels City's dramatic recent rise renders a lot of those statistics as irrelevant and is hoping the league leaders' difficult January continues.
City still hold a three point lead at the top of the table but have gone out of both domestic cup competitions since the turn of the year and been without some key players.
Moyes said: "I think all sides will go through periods of difficulty during a season and Man City are probably just in a bit of that at the moment.
"They have lost a couple of boys to the African Nations Cup and there have been a couple of disciplinary things which they see haven't gone their way. It can sometimes just upset the rhythm at the club.
"Let's hope it is upset because we are going to have to hopefully catch them on an off night and us play very well.
"Over the years we have always had quite a good record against Manchester City.
"The difference is they have improved, and they have improved from last season. You can see that from their league position.
"Their players have got better, there is more belief, more understanding playing alongside each other.
"We are coming up against a far better, far greater Manchester City side than even we played last year."
Relations between the two clubs have been strained in recent times, most notably during and after City's acrimonious £22million signing of Joleon Lescott from Goodison in summer 2009.
Moyes and City manager Roberto Mancini also clashed on the touchline during Everton's win at the Etihad Stadium in March 2010 but the Toffees boss has respect for his opposite number's work.
Moyes said: "I think Barcelona might be a better squad but I don't know if there is a more expensive squad.
"It has been accumulated very quickly and to be fair to Manchester City, they have done a good job, they have done it really well.
"They have got themselves a team which is going close to winning the Premier League."
Despite that, Moyes expects his team - trailing in a lowly 14th place 28 points behind City - to compete fully, as they did against them in the reverse fixture last September.
He said: "We lost 2-0 at the Etihad Stadium but I thought we played quite well on the day.
"We limited them up to 75 minutes. We didn't have many attacking options to cause them many problems but at that time they were scoring freely.
"We lost a goal when we gave the ball away in the middle of the park then they scored in the 90th minute to make it two and (Marouane) Fellaini had one kicked off the line in the last minute."
Everton's form ahead of the contest is indifferent with just one win from their last six in the Premier League. The Merseysiders have also managed just three wins from their 11 home fixtures.
They at least go into the game in good heart after seeing off Fulham 2-1 with a hard-working performance in the FA Cup fourth round last Friday.
Moyes said: "We are in the next round of the FA Cup. It doesn't always matter how you get through, you just want to get in.
"Hopefully, if there is any way it helps us towards the league, then great. You can never tell but hopefully the result gives us a bit of confidence."
