It's my understanding that the Roman Catholic, Greek Orthodox, and Coptic Orthodox denominations claim to be the true Holy Apostolic Church.
True. Also, the Assyrian Churches of the East. That's all that I know of.
Which one is it, exactly?
....and why does it matter?
I prefer to be in the church established by Jesus Christ. The one in which the gates of hades won't prevail. (Matt 16:18). Is there salvation outside of Christ's church? I think so, but I would rather be in Jesus' church. Wouldn't you?
First the church is estblished in the heart of every true believer that loves Jesus as Lord. This is not an instututional thing. Its not an order or hierarchy nor denominational and when the vatican and church buildings are a burning ruins and the devil does his best to stamp you out your faith will not die because our salvation is eternally established in the heart and the gates of hell shall not prevail against it.
Forasmuch as ye are manifestly declared to be the epistle of Christ ministered by us, written not with ink, but with the Spirit of the living God; not in tables of stone, but in fleshy tables of the heart. 4 And such trust have we through Christ to God-ward: .( 2 Co 3:3-4)
9 And I will give them one heart, and I will put a new spirit within you; and I will take the stony heart out of their flesh, and will give them an heart of flesh: ( Eze 11:19)
And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever; 17 Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you. .( Jn 14:16-17)
6 Know ye not that ye are the temple of God, and that the Spirit of God dwelleth in you? (1 Co 3:16-17)
This is where the New Covenant church is established and the gates of hell cannot prevail against it