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The Eastern tradition always limited the word "sin" to "actual" (freely chosen) sin, which does condemn to hell, justly so.

Biblically, the eastern tradition wins:

The word of the LORD came to me again, saying, "What is it to you that you use this proverb concerning the land of Israel, saying, The fathers have eaten sour grapes and the teeth of the sons are dull? As I live," says the Lord GOD, "to you there is no longer any occasion to use this proverb in Israel. Behold, all souls are Mine. As the soul of the father, also the soul of the son, they are Mine. The soul that sins, it shall die. . . The soul that sins, it shall die. The son shall not bear the iniquity of the father, nor shall the father bear the iniquity of the son. The righteousness of the righteous shall be on him, and the wickedness of the wicked shall be on him."
--Ezk. 18:1-4, 20

We do suffer the natural consequences of Adam's sin--a cursed world, the inclination to sin ourselves, etc.--but none of us are sent to Hell for Adam's sin, nor cut off from God for eternity in Limbo (which would, in fact, be Hell).

Did you read the rest of what I wrote? The Eastern tradition always taught this; the Catholic West has taught it most of its history, with an interlude when it did not: Cyprian and Augustine and others in the West did not (said that original sin condemns to hell--based in part on the faulty Latin translation of Romans 5) but they are the odd-men out even in the West and the West has for a millennium agreed with the East that original sin does not condemn to hell.

It was Protestants who revived the "original-sin-condemns-to-hell" falsehood and even then, Arminius challenged that from within Protestantism.

So, "Biblically, the East wins" is silly. All sides in this debate were biblical. The issue was proper interpretation of the Bible and the Orthodox East and Catholic West agree; Calvin agrees with Augustine and Cyprian on this point agree but on very little else.