This same basic OP question was beat to death in the prior thread named Which denomination today is closest to 1st Century Christianity. (That thread was closed because the posting became uncivil.)
Though I am not tempted to believe that the oldest schismatics today are the original Christianity, still, I do believe the various old christianities tend to have many wonderful historic echos and doctrinal debri from early christian themes. I also think a study of the oldest schisms from rome, Africa, Byzantium, etc, are wonderful sources for historians trying to understand HOW certain doctrines were created, changed and how some were lost.
1) A Loss of prophetic leadership
I do not think that doctrinal accretions and evolutionary changes to the earliest doctrines was completely unavoidable. For example, once the last authentic apostle, John the revelator, died, then, all congregations such as Antioch, Rome, Jerusalem, Galatia, ephesus (and others not mentioned in NT texts...) were in the position of having no living source of apostolic authority nor prophetic revelatory guidance such authentic leaders [αποστολοι, etc.] had provided in the fledgling Jesus movement.
2) Early Doctrinal Immaturity of the Jesus Movement
Once the early congregations were "on their own" to make their own way as best they could without revelatory leadership it was inevitable that all would tend to stray in differing doctrinal directions.
Origen pointed out that the Christianity of his age had not yet decided whether God the Father had a physical body or not. Such a doctrinal immaturity was a difficult situation since many other types of doctrinal details were not spelled out for the christian movement which was coming under increasing pressure for answers to such questions from honest investigators and their antagonists alike.
3) Christianity attempting to better define itself
This lack of answers to simple doctrinal questions led to many early arguments and to a proliferation of multiple theories and further schisms were not unexpected. The ancient arguments over doctrines often reminds me of the very, very similar arguments we all see in modern religious and philosophical forums.
4) "Theologian derived religion" versus "Prophetic and Apostolic transmitted religion"
Various theologians attempted to fill the doctrinal gap left by the death of Apostles and Prophets. Though I believe many of these theologians were doing their very best to generate answers and theories and doctrines based on their best guesses and logic, I believe that theologian-derived religion was inferior to Prophet-transmitted religion that had existed in the early Jesus movement.
Some theories of the Theologians became more popular than other theories and took on the mantle of orthodoxy. It was a situation of later ecclesiastics and theologians attempting to "make do" and feel their way in the dark to a certain extent. It was the best they could do, given their circumstances.
I believe many early theologians' motives involved an honest and good desire to protect and "further christian aims as they generated ever more theories to fill the early gaps in knowledge though I am sure that ego and pride contaminated many of the early arguments over what was to be taught as orthodoxy .
The resulting doctrinal accretions and evolutions away from early simple doctrines are a study in the difference between the often well-intentioned theologians and the authentic inspirations of apostles.
5) The resulting doctrinal evolutions that resulted in multiple Christian Movements
Given a proliferation of various but specific systems of beliefs, it makes perfect sense historically, that doctrines would undergo evolutions.
a) Some simple, core doctrines would be kept perfectly intact
b) Some doctrines would evolve away from early versions (but still present in some form)
c) New Doctrines and practices would appear
d) Some early Judao-Christian doctrines would be abandoned and ultimately lost
6) The role of historical principles in answering the Opening Posts question
To answer the question regarding which modern Christian movement is most similar to the earliest Christian movement, one must FIRST define what the earliest Christian movement was like (else, there is no valid comparison.)
Legitimate and authentic history attempts to answer the questions regarding what early Judao-Christianity might have looked like; what its doctrines may have been; and what its authentic practices were and the meaning and purposes underlying those practices.
Modern religious historians are not simply left to arbitrary and modern interpretations of a few memorized biblical verses in a manner batted about in many of the arguments we see between christians arguing for their myriads of competing interpretations. There is a vast amount of early Judao-christian sacred and secular texts available to us. One can learn about what the early Judao-Christianities believed and what their beliefs and practices looked like by reading early Mishnas, early psalms/odes, early Christian Synagogal prayers, early christian diaries, the earliest discourses, early canonical texts that are no longer included in modern (or western) texts; epigrapha, etc, etc. This situation continues to improve.
7) A THEORETICAL "CUT AND PASTE" OF THE FIRST CHRISTIANITY IN THE TIME OF APOSTLES
a) Earliest Form of Organization apostles, prophets, bishops, elders, etc.
A hypthetical denomination that would be closest to first century Christianity would be (in my opinion) a "cut and paste" of the earliest church into our era. That is, to cut the 12 apostles and early prophets (with their on-going revelations) out of the first century and paste that sort of organization into our modern era.
b) Earliest forms of Christian Doctrine, earliest definitions of faith, baptism, etc
Cut the earliest doctrines regarding Gods plan for the spirits of mankind out of the earliest Judao-christian texts and paste those doctrines into this hypothetical denomination. Cut the earliest doctrines regarding Faith in Jesus, repentance, baptism, gifts of the spirit among their leaders and among the laity and paste them into this hypthetical denomination.
c) Earliest forms of Practices
Cut the earliest descriptions of Baptism, of ordination, of healing and miracles out of the early descriptions of Judao-Christianity and paste them into this congregation.
d) Ability to use the earliest texts of Judao Christianity
I think that knee-v (in the prior post), makes an interesting point regarding the earliest Judao-christian writings)
I have come to believe that a hypothetical modern Christian movement that resembles the 1st century Christianity will be mostly oriented to, comfortable with and able to use the greatest amount of the earliest texts in demonstrating their teachings while those less like the earliest Judao-Christians will find the earliest texts disorienting and inconsistent with their doctrines (and will thus be dismissive of the earliest texts and perhaps call the early Christians and their writings, "heretical").
If one cut and pasted early Texts into the midst of this movement, they should be able to make better and more comfortable use of such texts than the denominations to which early Judao-Christin principles would be completely foreign.
I think that, to discuss "which denomination" is most like the earliest christian movement, one will have to break the question down into discrete and specific comparisons such how close its organization is to the earliest descriptions of Christian organization, how close its doctrines of salvation are to those of earliest christianity (e.g. faith, repentance, baptism, gifts of the spirit; fruits of conversion, etc.), how close its practices are to the earliest Judao-Christians (baptism, eucharistic meal, etc), and how seamless the earliest Judao-Christian texts reflect and could be used by this hypothetical denomination.
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