Though commonly referred to as "pronunciations", like I have done above, I like to think of them as different accents, the type of which you would hear in any language by speaking to different groups of people: the English of Texas and London; the Spanish of Lima and Madrid. In essence, you would find a priest who reads Latin with this Italianate pronunciation, while a Classicist, though he may be familiar with both, would prefer the reconstructed pronunciation from the Golden Age of Latin (80 B.C.-14 A.D.).
Here I present to you my rendition of that reconstructed Classical pronunciation. Not having a recording of a Roman from that time period, there are some who will argue that we can never be sure of what the Latins sounded like. We have, however, the Romance Languages themselves, which tell us about their development from Latin, not to mention the accounts from Roman authors themselves, describing and prescribing the pronunciation of their language.
While I don't dislike the Ecclesiastical pronunciation, because, as I just mentioned, I simply consider it another accent of Living Latin (that is, Latin being used for communication purposes today), I do prefer the Classical one. I am confident that this is an accurate representation of the pronunciation of an educated Roman around the birth of Jesus Christ.
I will conclude by pointing out, briefly, the main differences between a Classical and an Ecclesiastical pronunciation. First, while some diphthongs are fully sounded in the Classical model, they are reduced in the Church pronunciation: Classical L.