Before using the same critique methods that one would use in judging Western artwork, one must have an understanding as to what an icon is, and what is its intended purpose.
An icon (from the Greek, εἰκών, eikōn) is an image. In the Orthodox Church it is specifically a religious image of Christ, a prophet, a saint, a scene from the Bible, or a scene from the life of a saint to be used in worship. It is important to note that when describing Orthodox icons, the Church describes them as being "written" as opposed to being painted.
Iconography in the Church dates back to the first century when the early Christians made icons of Christ, His mother, and the saints. Unfortunately, due to an iconoclastic movement in the seventh century which destroyed many icons, we do not have any icons from the first century. (The oldest remains are from the third and fourth centuries from the catacombs of Rome, and from the monastery of St. Katherine at Mt. Sinai.) However, Eusebius, Bishop of Caesarea in Cappadocia (260-340 CE) writes, “I have seen a great many portraits of the Savior, of Peter and of Paul, which have been preserved up to our times” proving that icons were used prior to the 4th Century. This testimony is especially significant since Eusebius was an Iconoclast. (The Meaning of Icons, Ouspensky and Lossky, p. 25)
The term in Greek for writing an icon is Hagiographia or "Saint Writing." This is because when the Iconographer (a person who writes icons) is making the icon, they are not just creating an image using brush strokes and paint; they are writing the Gospel with a brush.
The icon serves several purposes in the Orthodox Church. One is to educate the faithful about the beliefs of the Church. As different scenes from the Bible and the lives of the saints are portrayed throughout the Church, the faithful have a visual catechism before them. Images of the saints are set before us to be visual reminders of those who have "finished the race" before us, and who are to be Christian role models for us. The images of Christ are to remind us of the Incarnation. God the Word (in Greek, λόγος or Logos) was born of a virgin and became fully man and fully God so that we may be saved and join Him in heaven. In addition to this, the icons act as "windows to heaven" during worship as we join with the communion of the saints in worshipping our Lord. The icons draw us in, and help us to "lay aside all earthly cares" as we worship the one Triune God; Father, Son, and Holy Spirit.
In the book The Meaning of Icons, authors Ouspensky and Lossky explain how the Iconographer is to lay aside his own interpretation of how the events or persons being written are to be depicted:
“Portray in colours according to the Tradition;” says St. Simeon of Thessalonica, “this is painting as true as written in books and the grace of God rests on it, for what is portrayed is holy.” For this reason, the creation of an icon belongs to a category fundamentally different from that usually understood by this word. It has the character of catholic (soborny), not personal, creation. The iconographer transmits not his own “idea” (νόήμα), but “a description of what is contemplated”, that is factual knowledge, something seen if not by himself, by a trustworthy witness…For a true iconographer, creation is the way of asceticism and prayer, that is, essentially, a monastic way. Although the beauty and content of an icon are perceived by each spectator subjectively, in accordance with his capacities, they are expressed by the iconographer objectively, through consciously surmounting his own “I” and subjugating it to the revealed truth – the authority of Tradition.”…The freedom of an iconographer consists not in an untrammeled expression of his personality, of his “I”, but his “liberation from all passions of the world and the flesh.” (p.42-43)
With the style of the icon being dictated by Church tradition, this intentionally limited how much personal expression the Iconographer could impose on the icon he was writing. The idea was to make sure the faithful stayed focused on the subject of the icon, and not the talent of the artist.
If one exams icons of the 14th Century (and prior) in Rome, one will notice that they are very similar to those of the East. As Rome's theology changed, so did her religious artwork. The East, however, remained consistant in both theology and artistic depiction.
Icons have a very deliberate look to them. They are two dimensional images that take up the majority of the space, with very little concern for the background. This is because the sunset or mountains in the background will not help you attain your salvation; learning about the people and or events in the icon will. The symbolism is extremely important; an enlarged forehead represents wisdom, a small mouth represents humbleness, the red of Mary's veil represents her sorrow, the blue undergarment representing her virginity... on and on, each part of the icon carries a greater meaning. It's not just there for aesthetic purposes, but rather to teach and to lift up.
I remember reading in Pavil Florensky's Iconostasis (paraphrasing) that the iconostas is not there to create a barrier between us and heaven, but rather to draw us into heaven. (Unfortunately I don't have the book with me right now to cite the exact page number.)
While this post may not win you over to the aesthetic style of iconography, hopefully by understanding it, you will have a greater appreciation for it.