Is the Number of The Beast 666 OR 616? The actual Number of The Beast is only mentioned in Revelation 13:18;  In the Greek manuscripts, the  number is rendered  as χξϛ  or "six hundred and sixty-six".

In 2005 Oxford University's Ashmolean Museum revealed the discovery of the oldest manuscript (about 1,700 years old) of Revelation 13 which gave The Beast's number as 616 χιϛ. 

What is the more common belief between the two? What are some examples of Churches that belief in 666 and some in 616? Are there other interpretations this question does not consider?
The Scripture actually reads:


  Revelation 13:18 KJV  Here is wisdom. Let him who has understanding calculate the number of the beast, for it is the number of a man: His number is 666.


This in turn refers back to:


  Revelation 13:1 NKJV  Then I stood on the sand of the sea. And I saw a beast rising up out of the sea, having seven heads and ten horns, and on his horns ten crowns, and on his heads a blasphemous name. 


George Moorish in his Bible dictionary says:


  Besides the ordinary use of this word — such as distinguishing all animals from man, Exodus 9:10; Psalms 36:6; and as specifying quadrupeds from fowls and creeping things, Genesis 8:19 — the word is used symbolically for:


b. Great worldly powers, cheyva, qhrion, having different characters according to the symbolic creature specified, but signifying in each case the absence of all moral connection with God: used by Daniel for the four great kingdoms, Daniel 7:3-23; and in Revelation 13:1 to Revelation 20:10 for the revived Roman empire and for the Antichrist.

Taking a look back at Daniel chapter 7 we find a description of his vision of a similar beast:


  Daniel 7:7 NKJV  "After this I saw in the night visions, and behold, a fourth beast, dreadful and terrible, exceedingly strong. It had huge iron teeth; it was devouring, breaking in pieces, and trampling the residue with its feet. It was different from all the beasts that were before it, and it had ten horns.


Taken together many have concluded that This refers to a resurgent Roman Empire, and that Revelation 13:18 refers to the succession of rulers.

Others have concluded it refers to the Roman Catholic church and the Papacy.

Even others have taken:


  Daniel 7:4 NKJV  The first was like a lion, and had eagle's wings. I watched till its wings were plucked off; and it was lifted up from the earth and made to stand on two feet like a man, and a man's heart was given to it. 


To mean that it is a completely new World order which will rise up out of the sea of humanity.

So in answer to your question the number itself, which is the number of his name, and not the number of the beast is no consequence until we know what that name is. The name itself is unknown as far as Scripture is concerned, The book of the Revelation is purposely vague in that it is a revelation of the future; and some if not most of the book is yet to be revealed, and the reason for giving it to the Apostle John may well have been to warn us that we should be ever vigilant. 

The fact that there are contradictory references as to what that number actually is; is further evidence God is more interested in our being constantly vigilant that what the details of the Scripture are.

If we look at the opening of chapter 13 verse 18 we find that it says let he who has understanding do the calculation, and who fits that requirement?