The RC mode of thought on our redemption through Christ is legalistic in a cause and effect sort of manner in that every temporal sin must be repaid in temporal form despite Heavenly forgiveness. In this case Christ paid our debt in our place by suffering and dying in instead of us because sins could not be forgiven (and thus salvation could not be attained) if there was no one to pay the price. Furthermore, this is the reasoning behind RC indulgences, where when we confess (or rather RC's confess) our sins we are forgiven in Heaven but there is still a price to pay on Earth.
As Oriental Orthodox we know that Christ forgives sins in Heaven and on Earth and that this forgiveness is all encompassing and requires no residual temporal payment - this is not to say that there are not consequences that naturally occur on Earth. From our perspective, Christ was (and is) a sacrifice for our sins, in which He bore the full weight of our sins in order to reunite us with God. Yes, He did pay our debt in our place, but not because He had to, but because He loved us so much that He desired that none should perish.
Christ conquered death, in that He was the perfect sacrifice. Where the Jews sacrificed animals for their sins, those sacrifices were unable to provide salvation but were little more than an atonement for what they had done, unable to affect their hearts and did not prevent their deaths and imprisonment in Hell. Christ was perfect and blameless, and could not be contained in Hell; and upon His death He descended into Hell and reclaimed those souls who were imprisoned, vanquished Hell's monopoly over human souls, and rightfully claimed the throne of Judgement over mankind.
Prior to recent decades Theosis was not taught in Oriental Orthodox churches, but remains integral to the Eastern Orthodox churches as part of their tradition of hesychasm, mysticism and spirituality. I know that some will disagree with me on this, so I won't push it any further. We do believe that we are transformed by Christ and through the indwelling of the Holy Spirit, and that participation in the sacraments and keeping God's commandments is our contribution in our own salvation.