Van Persie will face his former club for the first time since defecting to Manchester United in the summer when the Gunners go to Old Trafford on Saturday.
RVP said: "I am the only player who can judge what it's like working with Arsene and Sir Alex.
"It is an absolute privilege to say that in my career I have had both these managers at the clubs I have played for. They are both icons as managers in football. They are both world class, one not more nor less than the other. I purely look at this comparison as a footballer. I look at the way they both work on the pitch, in training, at the club and off the field."
Van Persie added: "I had a fantastic time with Arsene. I enjoyed training, playing, talking and all the other times I spent with him. I love it that I now experience the same with Sir Alex.
"But what I love about both managers is that they came to their clubs for a good cause.
"They both wanted to be at the club for a really long time."