Well, I've done a bit of trawling and investigating and it appears to moi at least, that the 'Alexandrian' has the edge over the 'Byzantine':
In my travels I came across this interesting post:
The assertion that the so-called "Textus Recepticus" is of the Byzantine text type is just that, a bare assertion; It was made up from Second Millenium lectionaries that were convenient to Erasmus's Rotterdam home, not from any scholarly assemblage of first millenium manuscripts. Erasmus was unable to locate any Greek version of The Revelation so he simply translated from the Vulgate Latin into Greek.
In "Misquoting Jesus" Ehrman gives a better description of the process of analysis that leads to the conclusion that The Alexandrian Text type is the most reliable of the four identified text types; In brief, manuscripts are arranged into "families" based on identifiable similarities in their variants, and then as variants are determined to be older and younger a "family tree" can be arranged, with definite signs of "descent" showing where a variant became fixed into the "lineage". In brief, the Alexandria scriptorium shows clear evidence of higher quality control than the other scriptroria; This is to not surprising as history indicates that the Christian Community of Alexandria also enjoyed greater security and stability than the other communities of the pre-Constantinian Roman Empire.
Also, interestingly, the two oldest 'complete' manuscripts Codex Sinaiticus and Vaticanus are both Alexandrian.