The pope is commonly referred to by the respectful titles, "Holy Father" or "His Holiness". While it is true the Dalai Lama is also called "His Holiness", the two offices have different concepts on what constitutes holiness and have no relation other than the verbal title.
In that both positions are the heads of organizations which are respected by their own followers and many others in the world, each man is the head of a segment, but not all, of their "religious" group (Christianity or Buddhism), and each is the head of a temporal government - yes.
There are however many differences:
The Dalai Lama lives in a village in India
Tibet.
Tenzin Gyatso is the dharma name of His Holiness the 14th Dalai Lama (the present Dalai Lama).
His Holiness the 14th Dalai Lama crossed into India on March 30th, 1959.
His Holiness, the fourteenth Dalai Lama is still alive and well. The previous 13 incarnations are dead.
On Life and Enlightenment Principles of Buddhism with His Holiness the Dalai Lama - 2006 V is rated/received certificates of: Australia:PG
his Holiness the Dalai Lama is well know for his peaceful and pacifist life,this man would love nothing better than to see his country of Tibet be free of the communist rule.
His Holiness the 14th Dalai Lama has been received by Her Majesty the Queen Elizabeth II on the 18th of July, 1996.
His Holiness, the fourteenth Dalai Lama is still alive and well. The previous 13 incarnations are dead.
As His Holiness the XIVth Dalai Lama of Tibet
His Holiness the 14th Dalai Lama of Tibet's name is Tenzin Gyatso. But he has decided to step down. If the government excepts this, he will no longer be the Dalai Lama. He thinks that it will strengthen the government and modernize it. I will be sad but I respect whatever he decides!
His Holiness the 14th Dalai Lama, Tenzin Gyatso, was born on 6 July 1935.