The Portuguese lead Spurs to a 3-2 win against United in the opening weeks of the season, their first victory at Old Trafford since 1989, and a result which took some of the early pressure off the former Chelsea boss during his early days at White Hart Lane.
The Red Devils have been on a great run of form since losing to Spurs and now sit clear at the top of the Barclays Premier League. They travel to face Villas-Boas' side in north London on Sunday with the 35-year-old hoping to complete a historic double over United, who will come up against an even better Tottenham team.
"I think (we have improved) because we have got to know each other better," he said. "Obviously we had a new manager in place and lots of changes to the playing squad too. I think we've got a consistency - at that stage at the end of September we would have welcomed the most amount of matches as possible so as to get to know each other a little bit better.
"I think both teams have improved but United compete for titles, have great players in their squad and they come here fully motivated I think, so its going to be a hard game for us."
During those early weeks of Villas-Boas' reign as Tottenham boss it seemed easier for his side to perform well and collect points on their travels, with fixtures at White Hart Lane not fully convincing supporters he was the man to replace Harry Redknapp.
Spurs' first three home games of the season yielded draws against West Brom, Norwich and Lazio whilst Wigan won at White Hart Lane at the start of November.
But since then Villas-Boas believes his side have become stronger at home and, although he anticipates a strong challenge from league leaders United, he reckons they will also be in for a tough afternoon.
"What we've changed from the time we played United is that we have improved our form at home," he said. "That is something United will recognise. White Hart Lane is never an easy place to come to. We're also on a great run of results and we will create big difficulties to United if we approach the game in the right manner.
"They've been on an amazing run since our win at Old Trafford. We now play them when they are at their strongest and confident about their game with the return of important players like Vidic and Rooney. They come here at their maximum strength. If we start well, if we're focused on the task, with the players we have we can achieve a result."