The Alexandrian is represented by a handful of 3rd and 4th century manuscripts, and partially supported by readings from early NT writers and versions.
The Byzantine is represented in full only by the vast majority of later copies, of various origins, ranging from the 4th century to the 14th century, and also with partial support from early writers and versions, but with little or partial support from the earliest surviving manuscripts.
How did this peculiar situation come to pass?
A Data Transmission Problem:
All textual critics seem to agree on the basic processes involved in the historical transmission of the text (hand-copying):
1) bifurcation (isolation and splitting into local texts)These factors however, do nothing to explain the actual situation as found in the surviving manuscripts. None of the basic sub-processes above predict the formation of special, pure dead lines in special "pockets" of early manuscripts and the simultaneous failure of the majority of copies to preserve the readings.
2) divergence (independent insertions, substitutions and omissions)
3) mixture (corrections, cross-pollination between competing text-types)
4) evolution (updating of grammar, style,vocabulary)
5) data loss (individual copies inevitably containing errors)
As a result, textual critics diverge on just how much data loss occurred and where this data loss happened in various stages of transmission, and consequently how to evaluate the surviving evidences.
Some are optimistic that the essential message of the NT is preserved in its entirety among the multitude of witnesses to the text, in spite of individual errors and minor corruption throughout the manuscript corpus. In this view, the early manuscripts may reflect an unfortunate 'wildness' of text in some quarters, but that such inconsistent witnesses and the minority readings they contain have little real weight in the big scheme of textual transmission.
Others are skeptical and doubt that the true text can be found in the mass of witnesses. They feel rather that substantial corruption took place, and that the "true readings" will be found in a minority of surviving ancient manuscripts from dead transmission-lines, in particular the Alexandrian texts.
The case then boils down to this: Alexandrian or Byzantine. No serious textual critic suggests any other candidates for the original or early text. The whole debate is over the specific differences between the two basic text-types, and this is obvious from the two basic 'critical texts' offered by text-critical parties.
Although there are other early 'text-types' (like the 'Western') and other early witnesses (e.g. the Old Latin version), no large parties of textual critics are backing other horses.