There was an in-depth discussion on the Byz Forum titled, "Icon of the Holy Trinity" or words to that effect. It was quite a lively discussion, to be polite.
In short, Rublev broke longstanding interpretation of the Hospitality when he implied that it was a manifestation of the Holy Trinity and excluded Abraham and Sarah from the depiction.
My own vote for the best icon of the Trinity is with the Theophany icon. "When you were baptized in the Jordan, the worship of the Trinity was made manifest."
In Christ,
Andrew