Than the Roman Catholic and Orthodox Churches -- the Anglican Ordinarite. After all, the Ordinariate also encompasses Methodists and other English Protestant traditions that are offshoots of Anglicanism. At least the Anglican Ordinariate would respect the English heritage of the United States, and are better equipped than most ethnic jurisdictions of Orthodoxy and the neo-Yankee multicultural Roman Catholic Church to be inculturated into the Anglo-American cultures present in the United States. After all, how much inculturation would have to be done, since the Anglican Ordinariate is already Anglo-American? It is very likely that the Anglican Ordinariate respects the language, history, culture, and ethnic aspirations of the founding stock -- can the same be said of the Roman Catholic and Orthodox Churches?
One may wonder what the appointment of a Portuguese-American Roman Catholic as the ordinary of the Personal Ordinariate of the Chair of St. Peter portends for its future. If bishops should be familiar with the culture of their flock, then how else can one explain his appointment (besides his familiarity with the workings of the ordinariate, especially the process of creating its liturgical books) than the assumption of American cultural homogeneity (especially under the influence of civic nationalism)? (And the myth of the "melting pot" in the large cities which were occupied by members of the immigrant Church.)
One is reminded of the importing foreign priests to serve in Roman Catholic parishes by bishops to staff their undermanned dioceses. What sort of education do they have in the culture and customs of the people whom they serve? Knowledge of Church teaching is not enough; they should also know and accept the valid customs of the native peoples.
Anyway, back to the Anglican Ordinariate -- some of the converts bring with them the English choral tradition, and Anglican plainchant in English. I have not been impressed by what I have heard, at least in the form adopted by a certain Roman Catholic seminary on the east coast -- that seemed to delicate and not manly enough. Maybe there wasn't a good mix of voices of different ranges.
(How difficult would it be to adapt Anglican chant to the Byzantine rite?)