Most modern versions play the three: the first stanza, the fourth stanza, and whichever one they feel like. It’s incredibly inconsistent what people play for the third verse.
My personal favorite candidate for the third verse is the third stanza (“O come, Thou Rod of Jesse, free”), as I think it puts a very important twist on the song, focusing on the importance of “Emmanuel’s” (Jesus’) mission on Earth. It also is a nice rounding out of the song; it feels like those three together tell a full story.
O Come O Come Emmanuel is definitely a candidate for my favourite piece of music ever written. Not just the hauntingly solemn yet beautiful tune, but the call and longing of the people of Israel for the Messiah's first coming is still relevant today instead as a call for Jesus' second coming.