Windmill will accuse me of sounding like a broken record here, but the Baronius Press version, while it is the licit pre-Vatican II Divine Office and still approved for use alongside the EF Mass, is not in any sense “traditional”. It is basically the same Divine Office that was promulgated by Pius X in 1910 and was, at the time, a fairly radical reform of the breviary. In fact many of the “controversial” elements of the current LOTH had their precedents set by Pius X 112 years ago; 112 years is short time by Catholic standards.
Among those elements:
Matins reduced from 12 to 9 psalms
Psalms divided into equal length sections that required the composition of new antiphons for which no traditional Gregorian melody existed
Splitting up of the 3 traditional “Laudate” psalms (148, 149 and 150) which always concluded Lauds since the time of St. Benedict (circa 500 A.D.)
Moreover Pius X, unlike Paul VI, banned the previous breviary.
The breviary of the Benedictines, even it its current post-Vatican II form (reformed liturgical year, etc.) on the other hand, has used the same basic psalter schema for 1500 years and I think has a much deeper claim on the notion of being “traditional”. It exists in both pre- and post-Vatican II versions depending on whether the community uses the EF Mass (a very small number) or the OF Mass (more common; there are also other post-Vatican II monastic breviaries that do diverge quite a bit from the original schema).
That’s not to say there’s anything wrong with using it: it’s perfectly licit especially if you normally attend the EF Mass, as it is more congruent with the EF liturgical calendar. But does not, IMHO, have a right to claim being “traditional”.
It’s also quite a bit more work than the LOTH… which I think in spite of its flaws (and I acknowledge there are some) is a brilliant reform that not only encourages lay participation but makes it feasible for busy working folks with families.