Benitez, now interim manager at Chelsea, is set to receive a hostile reception at Goodison Park on Sunday, from fans who will not have forgotten one infamous taunt in 2007.
The Spaniard referred to Everton as one of the Premier League's "smaller teams" after they held Liverpool to a frustrating goalless draw at Anfield.
Overall, Moyes clashed 14 times with Benitez during the latter's six-year spell with the Reds. Everton only managed to win three of those games, all at Goodison.
"It was always tough because Liverpool had a great team," Moyes said. "It was always hard to get the better of them. They had a tremendous team, and still have.
"I think he (Benitez) always wanted to be in the Premier League. I think he enjoyed his stint here.
"I think, like a lot of people who come to this country, he enjoyed the honesty and the way the Premier League is played.
"I think he has bided his time to get another job."
Benitez has started to turn around the form which prompted Chelsea to sack his predecessor Roberto Di Matteo last month.
The Londoners have won six of their last seven games in all competitions, with the one defeat in that sequence being in the Club World Cup final.
The run has also included an 8-0 thrashing of Aston Villa and seven goals from the often maligned £50million man, Fernando Torres.
Moyes said: "I think it is a great club - they are European champions.
"If you go there you have always got a chance of winning games with the quality and level of players they have got.
"I don't think it is any surprise that Chelsea are winning games.
"He (Benitez) is doing a very good job. He has inherited a really good team, some very good players. You would expect him to win games.
"Fernando Torres is an excellent player.
"I don't know the goings-on at Chelsea and I don't know enough about Fernando Torres to give you any real valued opinion - I just know he has always been a really good player."
Moyes hopes to have midfielder Darron Gibson available for a game which could see Everton leapfrog third-paced Chelsea with a victory.
Gibson is eligible after he and West Ham's Carlton Cole successfully appealed against red cards for high tackles in last week's meeting at Upton Park, but he has been troubled by a thigh strain.
On the sending-off Moyes felt common sense had prevailed, even if he was not sure an appeal would succeed.
He said: "I wouldn't say it was expected but I think most people in football will have seen both incidents as yellow cards and not sendings-off. They got to the right decision in the end.
"He (Gibson) has been really important since he came. His record in the team is really good.
"He has done really well, we are pleased with him.
"But we are always looking for more from him. I think he has got a bit more in the locker and hopefully we will get that out of him."
Everton are fifth in the table at the halfway stage having finally shaken off their tag as slow starters.
The Merseysiders are now well placed to challenge for a Champions League place if they can repeat their strong finish of recent years.
Moyes said: "I think we have done okay, I think we have played well at times.
"I'm a bit disappointed in the middle of that we didn't get a few more victories when we maybe could.
"But we have been on a pretty good run and are pretty consistent in what we do.
"I can't ask for an awful lot more. The players have done really well."
Moyes was dismissive of fresh speculation concerning the future of left-back Leighton Baines.
A new report has claimed this weekend's opponents Chelsea are now interested in the England international but Moyes said he had not read it and "it will be wrong".
Meanwhile, the agent of John Heitinga has been quoted as saying the Dutch defender is unhappy at the club.
The 29-year-old has made just eight starts this season.
Rob Jansen told Voetbal International Radio: "Heitinga is certainly not happy with what's happening at Everton, and we do not hide it. We are looking for a solution.
"If an appropriate situation arises for a transfer, we will certainly not ignore it."