The only thing I can think of where it makes a meaningful difference is that without the stain or guilt from sin, an unbaptized baby would assumedly still be allowed into Heaven under the Eastern view.
Other than that, the consequences are the same. We are prone to temptation and sin due to the Orginal Sin of Adam and Eve.
However, rather than it being inherited, it is a consequence. It would kind of be like if one’s parent’s squander all their money and at their death, their house is taken by the banks.
The children do not inherit the debt of the parents but are left with the consequences of not having any money or a house left for themselves.
I think similarily the East believes that we did not inherit the sin of Adam and Eve but are likewise left with the consequences which from an Eastern perspective would be the fact that we will all age and eventually die before being reunited with God.
I actually like the Eastern perspective because in my opinion, choosing to mortally sin, really is a desire for instant gratification and a doubt in our Heavenly reward in Heaven.
Death is a scarry thought and even with a devout belief it is easy to think that God will understand or just in case God doesn’t exist one better do this and have some fun now and then if God does exists, which one may be almost postive that He does, God will forgive him. Stuff like that. So I think that is the Eastern Perspective of Orginal Sin, a fear of one’s own mortality and the temptation to sin that comes with it.