I don't want to get into a major discussion of textual criticism, but having done my dissertation on the textual history of Galatians, I can offer the following points.
The textual tradition for Galatians (and presumably the rest of the Pauline Corpus) divides very early into a Western stream and a Eastern stream. Codex Vaticanus and P46, usually considered "Alexandrian," are actually witnesses to a very early form of this Western stream, later attested to by Marcion (!), D (Codex Claromontanus in Paul), F, G, and the Old Latin. The best witnesses for the Eastern stream are Codex Sinaiticus (01) and 33. The Byzantine text is an outgrowth of one of the sub-branches of this Eastern stream, with a little influx of Western readings.
I avoided the shorter reading criterion precisely because of recent questions concerning its validity, and yet I still found the Byzantine text to be a fairly late stage of the text, characterized by harmonization, a smoother and less ambiguous text, and an avoidance of some of the non-classical particularities of the Koine. Theological changes, however, were neglible for this text. If any form of the text is undervalued, I argue that it is the Western. But for some reason, the Byzantine text get all the attention as the major alternative in America.
Since every major division of the New Testament has its own textual history, these findings won't apply to the Gospels, the Praxapostolos, or Revelation.
Stephen C. Carlson, Ph.D. (Duke, New Testament)