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.
Moyes said: "It was always tough because Liverpool had a great team.
"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.
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.