The Juventus skipper believes the two take a similar approach to man management and is taking Champions League inspiration from Dortmund and Atletico
The 46-year-old took over from Antonio Conte this summer and the veteran goalkeeper has praised the ex-Milan boss for his consensual manner with the players.
"Everyone has their own character," he told La Stampa. "There is no formula that guarantees victory, otherwise it would have been patented.
"There is the sergeant like Louis van Gaal and then there's those like Carlo Ancelotti, who look for direct contact, and they both know how to achieve success.
"Which style do I prefer? I was pleased with both approaches because I received an education that helped me to respect authority.
"It is up to the players to figure out how to interact with the coach so as to give their best. Ancelotti said that the coach must be one of the group, not above it. Allegri is like this and it is a quality that I like."
Buffon went on to say that his team-mates are taking inspiration from Borussia Dortmund and Atletico Madrid, who reached the last two Champions League finals, as they plan an assault of their own on Europe.
"In the past two years Borussia Dortmund and Atletico Madrid have reached the final," he added. "Surprises do happen, although it is strange to define Juventus like this."
The 36-year-old also considered Juve's main contenders in the league for the upcoming season and believes Roma's success in the previous campaign marks them as the biggest threat.
"After last year they begin with enthusiasm and awareness of being competitive and having strengthened," Buffon continued. "At the start they are our equals."