The Dalai Lama believes he is (or says he believes he is) the reincarnation of his predecessor, the l3th Dalai Lama. He is also said to be an avatar of the Compassionate Buddha. He is a nice man and a Nobel Prize Winner, but superstition remains superstition. There is no evidence credible enough to justify belief in reincarnation. (God is both willing and unwilling to be called by the name of Buddha. But by and large most Buddhists are better people than most Western "Christians".
The Pope claims to be infallible in matters of faith and morals on certain occasions, and is understood by most Catholics as infallible generally speaking. This is a popular misconception. The title "Holy Father" for a human being seems blasphemous to me. I respect the recent Bishops of Rome including the late Karol Wotyla and the present Joseph Ratzinger immensely and follow their cues, but I think the time has come for the bishops to practice shirtsleeve diplomacy instead of pomp and circumstance.
These are not honorifics that both men have chosen. Instead the honorifics, historically, were imposed on them by the masses. Gandhi was embarrassed when he was called "mahatma" or great soul by the Hindus. He had a more humble estimate of himself than that. I'd suggest the Dalai Lama and the Bishop of Rome, great folks that they are and to be heeded, take lessons in how to keep from becoming the idols of everybody's heart.