Nameless
Member
I think Varys sees Littlefinger as a threat because he knows he desires power and glory on a personal level and is willing to instigate chaos from the sidelines in order to acquire such things. Varys on the other hand wishes for security in his life and power but doesn't seem to care much for recognition, in fact would rather stay unknown, and would like to see stability in the realm for this reason, regardless of his allegiance. Varys dislikes war, like Stannis' invasion, as it poses a threat to his position. And he knows full well Littlefinger would happily instigate such wars while also being on the other side of Westeros.
I rather enjoy him, but he would see this country burn if he could be king of the ashes.