I think the Assyrians use the liturgy of Mar Addai and Mar Mari, which is very ancient. I don't think the Armenians ever used that one.
Being "next door" to the Syriac peoples, though, the Armenians did in ancient times develop some of the same customs and local traditions. For example, the unusual shape of our altars is similar to that of the Syriac Orthodox and I think Assyrian altars. Why our altars are shaped like that is lost in the mists of time, as the shape is very ancient. However, I've only noticed it among the Armenian, Syriac, Assyrian and Indian Churches. Also, Armenian and Syriac Christians don't have iconostases, and, although we have icons, we tend to use less of them than the Copts or EO's. Assyrians don't use them at all.
The article by Terian is about a fourth century correspondence between the son of St. Gregory the Illuminator and the patriarch of Jerusalem at that time. The correspondence is important to scholars, I think because it documents the fact that the Armenians looked to Jerusalem for guidance in a lot of matters. Evidently there are things, such as our calendar, lectionary and rites, which preserve aspects of the Jerusalem rite which would otherwise be lost. Some scholars will study the Armenian calendar, etc. to know what the Jerusalem calendar was like way back when. At least that is how I understand it:
http://www.orthodoxchristianity.net/forum/index.php/topic,16853.0.html
