Fair enough. Lets call a spade a spade - we're dealing with the pre-Vatican II liturgy, although some Western rite jurisdictions take some egregious liberties with it. More on that later.
The Roman liturgy as currently authorized for use in Antiochian Dioceses can be found here.
The "Rite of St. Gregory" in ROCOR can be found here.
Antioch appears relatively conservative in its adaptations of the Roman Rite. A proper epiclesis was added - a move that has little historical justification behind it, so far as the use of Rome is concerned. Otherwise, the Filioque was dropped, a move that would have made number of admirable Roman Pontiffs quite proud.
Otherwise, a quick reading leaves one with the impression that Antioch to the pre-Vatican II Missale Romanum when codifying its English translation. Allegedly, there is historical precedence of some Roman Catholic groups simply transferring the pre-Vatican II books over. Antioch seems to have run with the usage current at that time. The directory for the Western Rite specifically decrees that the rubrics governing the rite are the Latin rubrics of 1950. Comparing the the text of the Canon with the text found in the Missale Romanum, one finds no major alterations, save for the epiclesis. The prefaces are lifted straight from the Missale Romanum, including the "newer" ones introduced post Reformation, extending to the Preface of Christ the King introduced by Pius XI.
Without having seen the actual propers, I would argue that Antioch appears to have demonstrated some respect of the historic liturgy of the West. If indeed it is true that former or historically Roman Catholic groups have found a place within the "Western Rite" by merely importing the Roman books and continuing with the Traditional liturgy in Latin, all the better. Based upon the information provided in the directory, the propers appear to be taken from the English Missal when the celebration of the liturgy is in the English language. I would be interested to know what Latin text has currency.
By comparison, ROCOR's Rite of St. Gregory is, if I may be so bold, a monstrosity and an affront to anyone who has respect and reverence for the Western liturgical tradition. This is a Frankenstein's monster, garbling together bits of Byzantium, Rome, and even the unchecked fixation with antiquity that led to some questionable modifications of the Roman liturgy in 1970. I want to be very clear here - ROCOR's Rite of St. Gregory is positively offensive. Antioch's insertion of an epiclesis is questionable and perhaps not absolutely necessary for an authorized liturgy. ROCOR's changes plainly disparage the integrity of the Latin tradition for reasons we cannot begin to fathom. Tell me where you will find "I believe and I confess..." among a substantial example of the Western liturgical tradition. This is one example of an infusion of Byzantine elements that have no place in the Latin liturgy.
We should "shoot straight and speak the truth" here: ROCOR's Rite of Saint Gregory has no historical precedence - one is about as likely to encounter a liturgy like this in antiquity as one would the Novus Ordo. It is entirely something new, although I suspect there is a possibility it could sky rocket in popular given the current exchange of ideas were it marketed effectively.
It is difficult to say what the future holds for the traditional Latin liturgy. It plainly needs as many outposts of conservation as possible. Antioch's approved English text is agreeable, with some reservations as noted above. The crucial quality is adequate respect and implementation of the historic liturgy of the West, specifically, that of the Patriarchate of Rome.