Well--and this is coming from someone who converted to the Orthodox faith in spite of the Eastern Rite, who much preferred Western liturgy at the time, and who has since become a reader in an Eastern Rite jurisdiction (so I'm committed, happily, to the "other side") yet still retains a fondness and a friendship with the Western Rite parish in town (whew!)--I can tell you that some of the things that appealed to me were the streamlined liturgy (not as repetitive, much more linear in form and function, the solemn, quiet movements done in spoken (and not sung) voice, the austere, humble surroundings (that do include icons, btw, but just not as many, as imagery in general and iconography specifically didn't play as big a role in the West as it did in the East), the familiar chant/hymnography, the architecture and aesthetics--the sight of the gospel book being carried out in procession by the vested priest with crucifer proceeding is wonderful to behold--the bringing of Ash Wednesday and other pious western traditions into the Church and baptizing them with a full understanding of what they're for--all this and more is why the Western Rite can (although it remains to be seen if it will) be a welcome presence within the Orthodox family--a severed branch being grafted back into the Olive Tree of the Church, so to speak.
Hope this helps.
Rdr David