I know the Sunday that my priest was out of town, I attended Divine Liturgy at a Serbian church...because of the Church Slavonic. It was closer to Ukrainian and felt "better" than English. I was completely able to participate in the Liturgy. I cannot vouch how I would feel in a Greek church, as I've only been to one, once, and that particular service was in English.
As for the "Ukrainian" people who said it's all the same, I would venture they were born in Ukraine, but, weren't necessarily of Ukrainian heritage.
One must keep in mind that under Communism, being Ukrainian was discouraged. People were not allowed to speak Ukrainian. Books were written in Russian, not Ukrainian. Kids in school were taught in Russian, etc. Remember, if you were Ukrainian in that era, you often found yourself persecuted, exiled or killed. Therefore, it isn't surprising that this current generation is "confused". It'll take a few generations to get things back on track!