The following quotations are from the book “Amit Napoleon életrajzai elhallgatnak” (PDF file, “What Napoleon’s biographies hide”), written by the Hungarian priest Vilmos Tower. It was published in 1937 by the Szalézi Művek publishing house in Rákospalota, Hungary.

Portraits of Napoleon and Pius VI on Wikimedia
[About the similarity of the treatment of the captive Pope and the captive Napoleon]
a) Napoleon imprisoned the Pope twice (Pius VI in 1796 and Pius VII in 1809). Napoleon was also captured and imprisoned twice (1814 and 1815).
b) Napoleon held the Pope captive for a longer time in two places: at Savona and at Fontainebleau (no stay of less than a month and a half is taken into account). Napoleon was also held captive in two places: on the islands of Elba and Saint Helena.
[…]
d) The two Popes were in captivity for more than seven years (1798-9 and 1809-14), as was Napoleon’s captivity (06.04.1814.-03.01.1815. and 07.15.1815.-05.05.1821.).
e) The two popes were searched at the time of their capture. All their valuables were taken from them.
Napoleon had already been looted by the French themselves. His private fortune of 11 million francs, saved at the time of his mission to Elba, his crown diamonds, his famous set of cutlery, his many tobacco boxes and many other valuable possessions were taken from him without any right or justice. Then the British searched him. While disembarking the Bellerophon, he and his escort were searched most thoroughly and very rigorously. Gold, jewels and bills of exchange were confiscated.
At the time, Pope Pius VI even had his ring, the badge of his dignity as high priest, pulled off his finger. Napoleon was stripped of the badge of his dignity as a commander and general. One of the orders issued to the captain of the “Northumberland” was “Napoleon must be disarmed!” The most humiliating thing for a soldier, let alone a general and an emperor!
(p. 104-105)
[About the attempted forced abdication of the Pope and the forced abdication of Napoleon]
a) At Fonlainebleau, Napoleon called on the Pope and tried to force him to renounce his temporal rule. Later, in the same city, in the same palace and in the same room of the palace, the powers forced Napoleon to abdicate the throne.
b) Napoleon had promised the Pope a pension of two million francs a year in the event of his abdication (paragraph 3 of the 1813 Concordat). Under Article 6 of the 1814 Treaty of Fontainebleau, the Allied rulers had also agreed to pay Napoleon an annuity of two million francs, to be paid from the French treasury.
c) Napoleon never paid the Pope the 2 million francs as compensation for the Papal State which had been robbed from him. It is true that the Pope would not have accepted it either, as he had indeed refused the first instalment.
Not a penny of the 2 million in annuities in Napoleon’s favor, agreed under the treaty of April 11, 1814, was paid to the former emperor. (p. 106-107)

Main Street in Jamestown on the Island of Saint Helena by Luke McKernan, CC-BY-SA 2.0, here
Napoleon recognized the Pope only as the religious head of the Church, not as the holder of temporal sovereignty (a sovereign). Before various delegations he referred to the Pope simply as “a Roman priest”. […] He himself said on the island of Saint Helena: “It was my plan to put an end to the Pope’s temporal rule, to make him my vassal and to make Paris the capital of the Christian world.”
Well, the powers also forced Napoleon to renounce his sovereignty. On the island of St Helena, he protested against not being recognized and called emperor or sovereign, but only general, and it was this circumstance that hurt him most during his entire captivity. […] But all his protests were in vain. When the brave, self-sacrificing Bertrand, Napoleon’s “chief steward”, protested on behalf of his lord, the Emperor, against the treatment of his Majesty, he was told that England recognized no “Emperor Napoleon”, but only “General Bonaparte”. (p. 107-108)
Napoleon’s treatment of the captive Pope was inappropriately, insultingly, humiliatingly rude and harsh, heartless and unfair. At Fontainebleau, there was a moment when the Pope feared that the Emperor would seize him by the throat, so furious was he in his anger because the Pope would not give up on his principles. That is why the rumor that the Emperor had struck the Pope in the face was widely believed, even though the Pope himself had denied it.
Napoleon was treated in the same way. He protested against being treated like a prisoner. He invoked laws, spoke of treason and treachery. He raged. “Every day,” he complained, “they repeat their wish to humiliate and dishonor me.” (p. 111)
Napoleon, as we have heard, had the correspondence of the prisoner Pope strictly controlled. All letters sent and received by the Pope passed through the hands of the French government. The Pope was allowed to receive only the official French paper, or, at most, any other paper which favored the French interest. […]
Napoleon met a very similar fate at Longwood.
The letters received and sent by Napoleon, and indeed by each of his relatives, passed through the hands of the English governor. Napoleon wanted to communicate with Europe by sealed letters, but without success. […]
His mother’s letter was not delivered to the Emperor until a year later. […]
For a long time, the captains of ships arriving on the island of Saint Helena were obliged to present Sir Hudson Lowe with a list of all the books and newspapers on board, especially those of a political nature, in order to prevent any undesirable press product from falling into Napoleon’s hands. Care was taken to see that nothing fell into his hands, except a few books and newspapers which Lowe thought good for the purpose. So he got a few copies here and there of the Times or the Morning Chronicle and a few French papers with an anti-Napoleonic slant. O’Meara occasionally smuggled other kinds of newspapers to the Emperor (p. 122-123).
The author does, however, mention two positive things about Napoleon: he never thought of tearing France away from the Church. He asked the Pope for a priest while he was a prisoner, and the Pope sent one to him, and he seems to have died reconciled to the Church.