I can only speak for the LDS position (Ex-Mormon here).
Mormons believe the same thing about the Orthodox that they do about the Catholic Church: that it's an apostate church that though teaching many correct things, has fallen into error and has lost the proper priesthood authority to administer the ordinances of the gospel (what you guys call "sacraments").
Mormons believe in the "Great Apostasy" theology, and like many other restorations sects, they believe this alleged apostasy happened within a generation or two after the 12 Apostles. Since they believe this alleged apostasy occurred so early (long before the Great Schism of the 11Th century), the Orthodox are lumped right in with the Catholics.
Mormons and JW's typically only have opinions on what their audience understands. Since their audience is typically arrogant and ignorant Americans who have little knowledge of stuff outside the American culture, they don't need to have opinions on Eastern Orthodox.
I their (LDS) opinion, they do believe in the original church but that it died out when the last of the apostles died, because with them the true Priesthood was gone from earth and with it went any authority to govern the "true" church. This is what they refer to as The Great Apostasy. Then when Joseph Smith came along, the true priesthood was restored and thus the authority of the true church.
Religious people scare me. You should all be so ashamed to speak of your half cocked beliefs that you do it in secrecy. Not because you will be persecuted, but because you will be humiliated.
The Apostles didn't set up anything. Paul did. St Paul, that is. And what's Orthodox about the Eastern Christians? Have you seen the extravagant costumes they wear? And their elaborate ceremonies, and all that ring kissing crap? If Jesus (nice, but deluded) could return he would be horrified what has and is being done in his name. He was a simple man, with a simple message, and never claimed to be a god.
And as for the Mormons, they were set up by a guy who wanted to legitimize his penchant for screwing multiple women.
Jehovah's Witnesses and Mormons are American denominations. They have very little knowledge of the ancient Eastern Orthodox Church, which most eastern/middle eastern Christians belong to.
Both groups are barley "evangelizing" the places were Christianity started (Greece, Israel, the Middle East, etc.)
I highly doubt it they think anything specific about the Eastern Orthodox doctrine...or any doctrine beyond their own. As far as they are concerned, they are right and everyone else is wrong...period.
Of course that attitude is not limited to the Mormons of Jehovas' Witnesses. It's a very common affliction among the Abrahamic faiths in general.
The JW view is worse though both consider all groups not their own to be apostate
They do not believe that the Patristic Church of the Seven Councils( which was before the sad R Catholic/ E Orthodox split) was that of the Apostles but that the Church could not fend off the doctrinal corruption and "Constantinian paganism" and " the gates of hell" did prevail in spite of what Jesus taught
JWs have created a fantasy JW out of Arius and claim that they are descended fro those "true Christians"( Even though the Arian / Semi Arian Church of the Goths, let's say, was very much like that of its Catholic/ Orthodox rival in liturgy, etc and not at all in most areas like the JWs
LDS claim that all the Christian Churches were apostate and there had to be a "restoration" of authentic revelation and doctrine
They have no answer to the testimony of survival by the Orthodox Churches (Eastern, Oriental and Assyrian) or the catholic Churches from centuries of oppression and persecution in the Near East and Balkans, for example
Why yes, I DO believe that the Original "Church (if you must use that term)" that was set up by the "Apostles", having survived (nearly) 2,000 years of persecution, has some error.
After all, it's a little hard to "grow... in knowledge" if you are already right about everything!
But what has anything about the authentic and original "Church" got to do with the EOC? Perhaps you are confused.
I am not LDS o JW.. but the true church is found in the roman church and eastern orthodox churches. because these churches are apostolic.. the church of Rome was founded by Peter, Jerusalem by Saint James etc.
I am LDS and it is plain to me that the authority of the church resided with the apostles. Otherwise, why would they call new apostles to replace the ones that died? It is also clear that at some point, they stopped calling new apostles. When the last of the apostles died, the apostolic authority was lost from the earth.
John was one of the last living apostles. Listen to the hopelessness in John's assertion:
"Little children, it is the last time: and as ye have heard that Antichrist shall come, even now are there many Antichrists; whereby we know that it is the last time. " (1 John 2:18)
As far as John was concerned, the end was near. The apostles had been murdered - one by one. Their message had been rejected. The day of the anti-Christ was upon them. This day had been prophesied by Paul:
"1 Now we beseech you, brethren, by the coming of our Lord Jesus Christ, and by our gathering together unto him,
2 That ye be not soon shaken in mind, or be troubled, neither by spirit, nor by word, nor by letter as from us, as that the day of Christ is at hand.
3 Let no man deceive you by any means: for that day shall not come, except there come a falling away first, and that man of sin be revealed, the son of perdition;
4 Who opposeThnd exalteth himself above all that is called God, or that is worshipped; so that he as God sitteth in the temple of God, shewing himself that he is God. "
(2 Thessalonians 2)
Paul wasn't merely prophesying persecution. If this "falling away" amounted to mere persecution, then he would already have been looking for Christ to return. He was expecting that the church would become corrupt by some outside influence, before the return of Christ. Paul tells us more about this "falling away" in his letter to Timothy:
" 3 For the time will come when they will not endure sound doctrine; but after their own lusts shall they heap to themselves teachers, having itching ears;
4 And they shall turn away their ears from the truth, and shall be turned unto fables. "
(2 Timothy 4)
He isn't talking about any particular faction, but of the church in general. Rather than accept the pure gospel as taught by the apostles, the members would look for ministers who told them what they wanted to hear. What they wanted to hear is plain: the reference to fables is a clear reference to Greek philosophy. Paul was fortelling the corruption of the Christian church by Greek philosophy.
The only hope of the apostles, was the eventual restoration or restitution of the church in the latter days.
"21 Whom the heaven must receive until the times of restitution of all things, which God hath spoken by the mouth of all his holy prophets since the world began. "
(Acts 3:21)
This is to happen after the Roman empire splits into numerous smaller kingdoms:
"44 And in the days of these kings shall the God of heaven set up a kingdom, which shall never be destroyed: and the kingdom shall not be left to other people, but it shall break in pieces and consume all these kingdoms, and it shall stand for ever. "
(Daniel 2:44)
Then would the prophesy be fulfilled concerning Elijah the prophet:
"5 ? Behold, I will send you Elijah the prophet before the coming of the great and dreadful day of the Lord:
6 And he shall turn the heart of the fathers to the children, and the heart of the children to their fathers, lest I come and smite the earth with a curse. "
(Malachi 4:5-6)
"11 And Jesus answered and said unto them, Elias truly shall first come, and restore all things. "
(Matthew 17:11)
Certainly if there was something that needed to be restored, then something must have been lost. John states that the pureness of the gospel would need to be retaught through heavenly intervention:
"6 And I saw another angel fly in the midst of heaven, having the everlasting gospel to preach unto them that dwell on the earth, and to every nation, and kindred, and tongue, and people, "
(Revelations 14:6)
Well, we Mormons generally really dig their doctrine of thesis. Of course we use it differently - but we find a lot of ammunition in it for our notion that humans can become gods.
Yes, The LDS church is a restorations church, they believe to be a restoration of the ancient church established by Jesus Christ.
The Catholic Church and the Eastern Orthodox church before both of them broke apart claim apostolic authority through Linus the Bishop in Rome but there are no records that this bishop was given apostolic authority nor would it have been possible for the apostles to meet according to the established pattern to ordain new apostles at the time of Peter's death as they did at the time when they ordained Paul, since John had be exiled to the isle of Patmos. These churches do not have anyone serving in the office of the apostleship. So we owe a lot to them for preserving the traditions and many of the doctrines of Christianity, but they cannot be the Original Church set up by the Apostles, that church had Apostles and Prophets ordained by Jesus Christ.
These churches have also not survived 2,000 years of persecution, after many years of tremendous persecution Christianity became the state religion and the persecution stopped this is perhaps the worst thing that has ever happened to Christianity because it allowed pagan practices to be mixed with pure doctrines and it allowed the Christians who suffered like their Lord to become persecutors.