I'm sure others will have better and deeper things to say than I, but I'm under the impression that it's both. Christ's incarnation, life, death, resurrection and ascension are, first and foremost, a mystery. And as such, any language or metaphor we use will always be like seeing through a glass darkly. The Scriptures utilize both ways of speaking (and even more). Our sins are definitely "offenses" and it doesn't get much plainer than, "Therefore let it be known to you, brethren, that through this Man is preached to you the forgiveness of sins" (Acts 13:38). But the Scriptures also speak of it as turning from "darkness to light," from "death to life," from "Satan to God," etc., and all of these things are true as well.
I think one aspect of Orthodoxy's emphasis on the sickness/health aspect, is because it's much more human and immediate and relatable than a divine courtroom scenario, you know? We've all been sick, we all know what that feels like, we've all known people who've been destroyed by illness, and we all know the relief that comes from medicine and other remedies. And this understanding really can affect how you understand God and relate to Him. Do we feel closer to, and more loved by, a Physician that places his gentle hands on us with the balm of healing, or to a High Court Judge, staring down at us from his Judgement Seat, gavel in-hand?
The Physician scenario seems to jive more with the Christ we meet in the Gospels, too, and from the beginning, sin was always understood as that which brought about death, physically, literally, and not that which brought about guilt, somewhere "out there" or "up there" in the Court of Heaven.
I think, too, that this understanding makes the most sense when you consider what really happened when Christ assumed human flesh, lived a human life, "became sin for us" by absorbing the totality of the human condition and our estrangement from God, and took that to the grave to kill it forever. In our Baptism we are joined to Christ, we die with Him, we enter the grave with Him and we are raised to new life with Him. In light of this reality, it's interesting to note how St. Paul (from whom we get most of our "juridical" language) describes the nature of sin in our life and how it affects us. He says,
"For if we have been united together in the likeness of His death, certainly we also shall be in the likeness of His resurrection, knowing this, that our old man was crucified with Him, that the body of sin might be done away with, that we should no longer be slaves of sin. For he who has died has been freed from sin. Now if we died with Christ, we believe that we shall also live with Him, knowing that Christ, having been raised from the dead, dies no more. Death no longer has dominion over Him. For the death that He died, He died to sin once for all; but the life that He lives, He lives to God. Likewise you also, reckon yourselves to be dead indeed to sin, but alive to God in Christ Jesus our Lord. Therefore do not let sin reign in your mortal body, that you should obey it in its lusts. And do not present your members as instruments of unrighteousness to sin, but present yourselves to God as being alive from the dead, and your members as instruments of righteousness to God. For sin shall not have dominion over you, for you are not under law but under grace. For when you were slaves of sin, you were free in regard to righteousness. What fruit did you have then in the things of which you are now ashamed? For the end of those things is death. But now having been set free from sin, and having become slaves of God, you have your fruit to holiness, and the end, everlasting life. For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord."
This is not a courtroom scene, even though that declaration of "not guilty" is part of the picture. St. Paul says that, in light of what has occurred in reality, and what we have entered into sacramentally through our Baptism, we should not let sin reign in our bodies and we should not present our bodies as instruments of unrighteousness, not because we don't want to offend God again (although that is certainly part of it) but mainly because sin leads to death in a very real and concrete way; literally and physically and spiritually. Just like a disease.
We must fight sin, not because we don't want to become "guilty" again, but primarily because sin is a very real sickness that leads to very real death. In the courtroom scenario, our declaration is simply that, a declaration. It has no real bearing on the life that we live, because we still battle the disease of sin every day. We can, even after having been declared "not guilty" still become slaves to sin which is why, as St. Paul admonishes us, we need to not let it reign in our bodies, obeying its "lusts" (or "passions" as Orthodox often call them). Understanding sin as a sickness in need of medicine places it in the sphere of something that we can relate to, and even overcome, by participating in the grace of God through the mysteries of the Church. It's no wonder then, that since earliest times, the Eucharist has been called the "medicine of immortality."
This is probably one of the main reasons why Orthodoxy does not hold to the "once saved, always saved" doctrine so prevalent amongst many Protestants and Evangelicals today. When you view sin and salvation only as offenses and juridical declarations, of course it's easy to believe that once you've been declared "not guilty," that's all there is to it. But when you see sin as the very real disease that it is, and something that doesn't just disappear after our Baptism, you see it as something you're going to have to battle for your entire life.
Yes, our sins have been forgiven and we have been declared "not guilty" but we still have the power to infect ourselves and "present our members as instruments of unrighteousness to sin" bringing that deadly disease back into our bodies. And that can, obviously, still kill us and why can die, separated from God because we chose death over life.
Things are really hanging in the balance, and we have very real choices to make, choices that are literally life or death. And I personally don't see how the gravity of that reality can adequately be communicated to people when we only speak of sin in terms of offenses and declarations and statuses, even though it can be helpful to understand it that way and the Scriptures use that type of language.
This is the beauty of Orthodoxy, in that it paints the whole picture and places before us the truest and deepest understanding of reality.