Almost* all liturgies will be very similar in structure. The differences, however, are not insignificant. After all, there must some accounting for the fact that the average Coptic Orthodox (Basilian) liturgy is about three to three and a half hours, while the average Roman Catholic Mass is about an hour or an hour and fifteen minutes (and, from what I understand, the usual EO Byzantine liturgy is somewhere in between the two). So, without having the time (or the necessary texts) to do a side-by-side comparison, we can say that the Roman Mass is, from our perspective, at least quite condensed or abbreviated. While I have not been to a Roman Catholic Mass since converting to Orthodoxy, Orthodox friends of mine who have attended (because they have RC girlfriends) describe it similarly. Whether this makes the Orthodox Church closer to that of the apostles or not is debatable, but what we can say based on what we know of the development of our own liturgies is that the Liturgy of St. Basil (the most commonly celebrated of the Coptic Orthodox liturgies; I’m referring to it because that’s what I’m most familiar with) is actually an abbreviated form of the liturgy that was introduced to Alexandria by St. Mark himself. So in that way it is directly tied to the apostolic church, although it may just be showing the fact that our liturgical development as Orthodox Christians was arrested circa the 5th century (the core of the Basilian liturgy was fixed by the fourth century, but the parts around it are probably later; the Coptic form is based around the earliest complete manuscript, in the Sahidic dialect and dated 7th century AD; Byzantine versions are roughly one century later, but all the different versions [Coptic, Byzantine, Armenian, etc.] are hypothesized as coming from the same original source dating back to at least the time of St. Basil himself). Whereas the Latin Church has continued, for whatever reason, to develop its liturgies via subsequent councils and whatnot until they have what are known today as the Tridentine Mass (codified 1570) and the Novus Ordo (from the 1960s).
So I think the differences are more revealing about our attitudes toward the liturgy and broader issues of ecclesiology and Church governance than whether or not a particular church is apostolic. All churches which were founded by an apostle are apostolic, at least in the most minimalistic sense of the word (i.e., not as Orthodox understand this concept). But that is not a guarantee that they will have any particular form of liturgy.
*- The Anaphora of Mar Addai and Mari, used by the East Syrians, is also quite old, maybe even older than the above described Basilian liturgies, but it lacks in its oldest extant manuscripts (c. 10th century) any form of the words of institution common to all other liturgies used by the ancient churches.