The Pulitzer for drama has a history of choices that particularly have not stood the test of time very well. Some of the choices seemed wrong or even stupid at the time, occasionally to the judges themselves. And unlike the Pulitzers, the people who vote for the Drama Critics Circle award are the ones who have the final say. Their choices do not get overruled by some stupid board or committee.
Which is not to say that I always agree with Drama Critics Circle but I think its history is at least slightly better than the history of the Pulitzer for drama.