Bookmakers installed Moyes as the odds-on favourite to replace Harry Redknapp in June, but Daniel Levy appointed Villas-Boas ahead of the Scot despite his excellent record at the Merseyside club.
Everton had come dangerously close to relegation through the back end of the 1990s, but Moyes' appointment in March 2002 signalled a huge turnaround in the club's fortunes.
The Scot, whose only previous experience in management had come at Preston, led the Merseysiders to fourth in 2005 and has only finished outside the top eight twice during his nine full seasons in charge.
Villas-Boas, who takes his team to Goodison Park on Sunday, thinks Everton would be in a much worse position had the 49-year-old not taken the helm 10 years ago.
"He has done tremendously well," the Tottenham manager said.
"He has changed the mentality of the club. They went through incredibly difficult situations financially and has always built strong teams.
"His scouting is perfect, his training is perfect, the way he motivates his players also makes a difference as you see them on the pitch and they are extremely competitive.
"His teams always seem to improve year after year and that is not always the case. Going to Goodison Park is one of the toughest games."
Villas-Boas has bad memories of visiting the Toffees. Last season his Chelsea team lost 2-0 at Goodison Park and little over three weeks later the Portuguese was sacked.
But after a shaky start, Villas-Boas has started to rebuild his reputation at Tottenham, who are now firmly in the hunt for a Champions League place following a run of three straight Barclays Premier League wins.
Confidence is high in the Spurs squad, but Villas-Boas knows it is vital his team maintain their good form going into the festive period.
"The Premier League is very, very tight between third and 10th," the former Chelsea boss said.
"Obviously we want to do well at Everton but understand that it is going to be extremely difficult.
"It is one of the most difficult grounds to go to, they are fully rested, but we have played in midweek.
"But we want to do well and take something out of there and continue with the momentum we have going."
Everton have only lost one of their last 10 games, although their last three results have been draws.
Marouane Fellaini's eight-goal scoring spree from midfield has played a big part in Everton's good form this season, and Spurs defender Kyle Walker knows shackling the Belgian will be key to the visitors' chances of success.
"Marouane Fellaini is a real handful," the England right-back said.
"He's mobile for a big guy, gets the ball down and they go through him.
"They've good players, lots of internationals and it will be difficult. Ever since I've played in the Premier League, Everton is always one of the tough games.
"But our centre-backs Jan (Vertonghen) and Steven (Caulker) are fantastic and hopefully if we can keep a clean sheet then Jermain (Defoe), Emmanuel Adebayor or Clint (Dempsey) can go and get us a goal.
"If we continue playing how we've been playing and those three keep scoring, then we've got every chance."
Villas-Boas looks set to recall Hugo Lloris in goal after giving Brad Friedel a run out in Tottenham's Europa League win over Panathinaikos on Thursday.
Gareth Bale is unavailable due to a hamstring injury and Michael Dawson also looks unlikely to play due to a similar concern.
Dempsey will probably start in Bale's place on the left, leaving Adebayor and Defoe free to resume their partnership up front.