The short answer may be: Depends largely on whether you ask a Catholic or Orthodox Christian, and how familiar that person is with their Catholic or Orthodox "cousin." There is a good amount of scholarship on either side of the issue.

Certainly, there is much about either Church that differs today from the pre-Nicean form... beside structure and organization, there are apparent differences in doctrine. Heck, their common names are different. And either Church has points "for" and "against" in each column.

The Catholic and Orthodox Churches aren't simply "one" Church, but a combination of many Churches. There are, presently, 23 Churches that make up what we would call the "Catholic Church," with the Roman Church - the one most would normally (and technically incorrectly) think of as being "the Catholic Church" - being only one of these. Contrasted with this, there are 13 Churches that make up what we would call the "Orthodox Church," with the Greek or Russian Churches being the "typical" Church one would imagine when using the term "Orthodox." For the purpose of your question, we'll discount the Oriental Orthodox (6 Churches), who split while what we now know as the Catholic and Orthodox were still united following the Council of Chalcedon in the 5th century.

As a matter of hierarchical structure and organization, the Roman Church remains the chief See within it's communion. This isn't a change from it's pre-Nicean nature, when the Roman Church would have been recognized - if not having universal, extra-ordinary jurisdiction over all the other Churches - as the highest ranking Church in the West. Contrasted with the Orthodox, this would be a "point" in Rome's favor given the status of the Church at Constantinople now being "first among equals" in the Orthodox Church, while pre-Nicea (and for a time, post-Nicea) this would have been the Church at Alexandria. Canon 6 of the Council of Nicea - itself a point of dispute between Catholics and Orthodox - makes this clear. Further points may be scored by the Catholics in the category of hierarchical structure and organization as many of the Orthodox Churches now recognized as autonomous did not exist as such pre-Nicea - Russia being the prime example, as it is by far the largest of all Orthodox Churches and wasn't formally recognized as independent until the 16th century.

Hitting on this same issue - that of the holistic organization of either the Catholic or Orthodox Churches - one can see a distinct difference in matters concerning doctrinal discipline, specifically the calling of ecumenical councils. These are the Church's primary means of sorting through dogmatic or juridical disputes (i.e. heresies or jurisdiction/discipline); the Council of Nicea was, for example, one such council (and perhaps the first if you don't count Jerusalem). Since the 11th century schism "defining" Catholicism and Orthodoxy, the Catholic Church has organized 13 major councils dealing with either dogmatic or juridical disputes. The Orthodox have organized none. As a mark of structure and organization, this is an additional "point" in Catholicism's favor.

That said, the nature of the hierarchical offices in either Church has changed as well. For example, it is now the custom for the Bishop of Rome - spiritual head of the Catholic Church - to be elected by the College of Cardinals, which is an innovation of the 11th century, whereas the Patriarch of Constantinople - spiritual head of the Orthodox Church - is elected by the Synod of that Patriarchate. While both are elections, the nature of the College of Cardinals as a group of hierarchs from different Churches (not all are Roman Catholic; there are for example Greek Catholic Cardinals) would tip the balance slightly in favor of the Orthodox, despite the body of either group being comprised of individuals from a greater geographic expanse than pre-Nicea. This is only speaking strictly about the situation today, as in the past the Orthodox Patriarch of Constantinople may have been appointed, for example, by the Ottoman Sultan, and the election of the Bishop of Rome may have been influenced by Western political powers; the result of either struggle (secular influence in the Catholic or Orthodox election) tipping the balance slightly in favor of Rome. As well, bishops within the Orthodox Churches are typically elected by members of the surrounding Churches - as opposed to the Catholic Church, where this practice exists only in the Eastern Catholic Churches; in the Roman Church, bishops are appointed by Pope following a lengthy vetting process. This being the case, the near-universal election of bishops in Orthodoxy would tip the balance for a "point" in their favor concerning historical precedent.

Theologically, the answer you will receive may depend largely on the source.

Certain members of the Orthodox Churches may tell you that the Catholic Church has entered into a kind of heresy, and that this justified the 11th century schism that except for a few brief periods persists until the present day. I have had certain Orthodox Christians - particularly those within the Antiochian Church - comment that Catholics were not even truly Christian due to these presumed errors. Whereas the general consensus "seems to be" - and this may be the best answer one can give, given Orthodoxy's lack of a unified statement concerning the subject - that while the Catholic Church retains valid sacraments and orders, the Latin addition of the filioque into the Creed (roughly 6th century) is a classic (one might say the classic) Orthodox "proof-text" concerning Catholicism's doctrinal innovations. Other "major" obstacles may include the Catholic dogma concerning Papal infallibility (formally defined in the 19th century) and the canons concerning Papal jurisdiction, while some "minor" obstacles may be the Catholic understanding of purgation or the Dormition of Mary.

Similarly, a Catholic would have bones to pick with the Orthodox - and for reasons the Catholic may consider far more substantially "doctrinal" than the filioque (which many theologians no longer consider a major binding issue) - as being reasons the Orthodox are now far apart from the pre-Nicean Church. Among them would be the Orthodox view on divorce, multiple marriages, and contraception, which do not mirror pre-Nicean practice.

Theologically, it would be difficult to award any clear "points," as it were.^1

The last category may be the liturgy - and there, once again, it gets difficult. Either Church contains Rites "pre-dating" Nicea. Where the Orthodox may point to the Roman Church's Ordinary Form of the Mass as being relatively new - a result of the Second Vatican Council in the 20th century - the Catholic could just as easily point to many of the Rites in the 22 other Catholic Churches as being as ancient (or the same) as anything the Orthodox have to offer and, further, that the evolution of the liturgy in the West actually reflects the historical reality that existed pre-Nicea better than the rigid cultural conformity of Orthodoxy in the East: that is, as Christianity spreads, the liturgy spreads with it - whereas Eastern Christianity essentially "stopped growing" beyond cultural boundaries, Western Christianity has not, and the Roman Rite better reflects that.

^1 ^I ^am ^Catholic; ^I ^consider ^the ^Catholic ^argument ^stronger, ^but ^presented ^as ^a ^matter ^of ^"scoring ^points" ^for ^the ^purpose ^of ^answering ^the ^question, ^am ^sticking ^with ^this ^statement. ^Oceans ^of ^ink ^are ^spilled ^on ^these ^topics ^and ^there ^are ^good ^arguments ^on ^either ^side.

While I appreciate the question, I'm afraid it may be coming from a slight oversimplification of the pre-schism Church. Before the Great Schism, there had always been differences between the Eastern and Western Churches, both theologically and liturgically (e.g. the Quartodecimanist controversy under Pope Victor). After the Schism, each Church, East and West, followed pre-schism trajectories in their developments, and both of these are ultimately traceable to the "Nicene Church" (which might more aptly be named pre-schism "Chalcedonian Christianity").

For instance, the Augustinian formulation of Original Sin, so foundational for the Western Church, found little traction in Eastern theology from the beginning. The theology and character of the Western Church owes much to this development, and the Eastern Church, operating under a soteriological framework of theosis moved along a different, if ultimately compatible, path. Both of these developments and the directions they took the Eastern and Western Churches have a right to be considered as equally being grounded in "the original Nicene church of the Roman Empire".

Furthermore, religions are never static ideologies, and both Orthodox and Catholic Churches have 'changed' throughout their long histories. To answer your question is to consider something that is by nature hard to quantify-- how do we measure whether one Church has departed more from the "original" (even assuming such a unified original, which is an incorrect assumption) theology? Both Catholic and Orthodox Churches hold on to the doctrines and anathemas expressed in the pre-Schismatic councils, so measuring difference by departure to original doctrinal formulations is not possible in this instance. Perhaps we might ask how much each Church has "added" to their doctrinal and liturgical edifice compared to their pre-Schism history? This is again a very difficult thing to quantify-- to what extent, for instance, should we consider the theology and usage of Icons by the Eastern Church a departure-from-addition to the "original"? Is the Orthodox teaching of the Dormition of Mary closer than the Catholic teaching of the Assumption of Mary to the "original" Marian theology? Again, there was no "one" original Marian theology, for instance, and we have a clear and distinct Western take on it as early as e.g. Jerome, which differed from the later (but still pre-Schism) John of Damascene, an Eastern theologian who influenced, well, how the Eastern Church formed.

To summarise, the theological and liturgical differences between the Catholic and Orthodox Churches were latent in the pre-Schism Church to begin with, and thus it is almost impossible to answer your question except by a tentative: "neither, and both".

You might also have luck at /r/academicbiblical

How do the orthodox churches view gnosticism? As I understand it, the Roman Catholic Church only removed any gnostic practitioners after the tenth century.