Now, with a persona such as Silence Dogood, it is somewhat evident why a male (Benjamin Franklin) would choose a woman (Silence Dogood) as his persona. My best guess is that Franklin uses his knowledge as a male to illicit a male argument by speaking satirically as a woman.
However, with the stand-up bit performed by Eddie Izzard, the choice of persona is a bit more curious. Izzard, a male, is crossdressed as a woman yet his comedy material isn't exclusively gender-based. He speaks, at least in the piece we viewed, of the varying views and actions of religious affiliations. Yet, why is he dressed as a woman? My thoughts so far are that it is a relaxing, absurd persona much like a clown. Why is a clown funny? Well, yes they do perform tricks but their dress and make-up exude light-heartedness and levity which therefore sets the audience more at ease and more susceptible to laughter. I think the same sort of process is occurring with Eddie Izzard stage presence. Much of his material could be interpreted as borderline offensive to some (I personally enjoy having my religion ridiculed and joked about). Therefore, either to avoid offending too many people or to create an atmosphere more open to laughter, Izzard dresses as a woman as if to say "I am crossdressed, I am an adult clown, Try not to take everything I say too personally because after all, it's coming from a man dressed as a woman".
While some persona roles may have high-order satire intentions, I believe that some, like Izzard's, are meant to let the audience know that they are going to hear jokes, not vicious tirades.