TL;DR
=====

The summary from the following book is that:

 - Oral transmission of the Early Buddhist Texts (EBTs) were very reliable in different schools.
 - Even if there is difference in content between the Nikaya and Agama versions, they are all doctrinally identical.
 - There is a very high degree of correspondence between the Nikaya and Agama versions of Majjhima Nikaya, Samyutta Nikaya and Digha Nikaya.
 - All texts which are almost word-for-word identical between the different versions, although in different languages, were authored before the Sthaviravada-Mahasanghika split.
 - Anguttara Nikaya and Ekottara Agama are structurally identical but have significant content differences. The Ekottara Agama is said to be unfinished and contains proto-Mahayanist additions.
 - Other EBTs which are part of Khuddaka Nikaya have a common core, but the contents can be quite different, between different schools.
 - The Abhidharmas are even more divergent between the different schools.

Details
=======

From [The Authenticity of the Early Buddhist Texts][1] by Bhikkhu Sujato and Bhikkhu Brahmali:

> We possess EBTs from a substantial variety of ancient Indian Buddhist
> schools, including the Mahāvihāra (modern-day Theravāda) of Sri Lanka,
> the Dharmaguptaka, Mahāsāṅghika, Mahīśāsaka, Mūlasarvāstivāda,
> Sarvāstivāda, and others of uncertain affiliation. **A century of
> detailed study has consistently shown that they are essentially
> identical in doctrine irrespective of transmission lineage.**
> 
> With corresponding footnote:         
> > The only complete set of EBTs is
> > the Pali version of the Mahāvihāra. Of the other schools we possess
> > EBTs in a variety of degrees of completion, from a majority of the
> > texts of the Sarvāstivāda, to only a few scattered Suttas and the
> > Vinaya of the Mahāsāṅghika. In the case of the Mahāsāṅghika, this
> > would change significantly if it can be established that the
> > Ekottara-āgama in Chinese translation (T 125) belongs to this school.
> 
> The great Belgian scholar Étienne Lamotte says ]: “However, with the
> exceptions of the Mahāyānist interpolations in the Ekottara, which are
> easily discernible, the variations in question [across the lines of
> transmission] affect hardly anything except the method of expression
> or the arrangement of the subjects. **The doctrinal basis common to the
> Āgamas and Nikāyas is remarkably uniform.**” This is in stark contrast
> to non-EBT texts.
> 
> ...  In 1882 Beal described detailed correspondences between Suttas in
> Chinese and Pali (in Beal, Samuel. Abstract of Four Lectures On
> Buddhist Literature in China. Biblio-Life, 2010.). He accurately
> predicted that “when the Vinaya and Āgama collections are thoroughly
> examined, I can have little doubt we shall find most if not all the
> Pali Suttas in Chinese form.”
> 
> Recently, in his detailed and thorough Comparative Study of the
> Majjhima Nikāya, **Anālayo shows that all significant aspects of early
> Buddhist doctrine are the same across all extant textual transmissions
> of the Suttas of the Majjhima Nikāya** (in Analayo. A Comparative Study
> of the Majjhima-nikāya. Dharma Drum Academic Publisher, 2011). Among
> the parallels to the Suttas of the Pali Majjhima Nikāya, the most
> important textual source, due to its completeness, is the
> Sarvāstivādin Madhyama Āgama preserved in Chinese. The Sarvāstivāda
> and Theravāda lineages must have separated approximately at the time
> of the Asokan missionary activities. This means that these texts have
> been transmitted separately for almost 2,300 years, including a period
> of separate oral transmission that lasted several centuries. And yet
> the doctrinal content is for all intents and purposes identical. This
> shows how conservative and careful the individual schools were in
> preserving the EBTs.
> 
> Moreover, this conservatism must have been inherited from the more
> unified—both geographically and doctrinally—form of Buddhism that
> existed prior to Asoka. There is no reason to imagine that the
> separate schools would all be conservative in preserving their
> canonical texts unless they had been conservative prior to their
> separation. Since comparative studies show that the **core doctrinal
> material of the EBTs has been reliably transmitted for almost 2,300
> years, the reasonable inference is that it was reliably transmitted
> also in the first 150–200 years of Buddhist history.**
> 
> In addition to the full scale study of the Majjhima Nikāya, there have
> been multiple smaller studies of various parts of the EBTs. **These have
> confirmed that all the EBTs share a similar level of agreement to what
> we find between the Suttas of the Majjhima Nikāya and its parallels.
> Such studies have been carried out for substantial portions of the
> Saṁyutta Nikāya/Saṁyukta Āgamas, and to a lesser extent for the Dīgha
> Nikāya.**
> 
> Caution needs to be exercised, however, regarding the **Ekottara Āgama,
> which is nominally the collection corresponding to the Pali Aṅguttara
> Nikāya. Although it shares some significant structural features with
> the Aṅguttara, the content is often very different.** The text is highly
> erratic and internally inconsistent, possibly being an unfinished
> draft. Scholars agree that it includes **proto-Mahāyānist additions**,
> thereby establishing its late date of completion compared to the rest
> of the EBTs.
> 
> This high degree of correspondence among the EBTs across different
> lines of transmission does not exist for any other texts of the vast
> Buddhist corpus. **Even in the stylistically oldest part of the Khuddaka
> Nikāya, such as the Sutta Nipāta, the Udāna, and the Dhammapada, there
> is substantial divergence between the schools.** This is despite the
> fact that these texts do have a common core, which is found across the
> different traditions. With texts such as the **Abhidhamma, despite a
> small common core, the divergence is even greater**. But the vast
> majority of Buddhist texts are exclusive to the individual schools and
> do not have any parallels at all.

And also:

> ..... The first doctrinal split in the Buddhist monastic community was that
> between the Sthaviras and the Mahāsāṅghikas. Because this was the
> first split, some scholars, such as Edward Conze and A. K. Warder,
> have suggested that material that is common to both these groups of
> schools be regarded as the most authentic.
> 
> With corresponding footnote:          
> > See Conze’s Thirty Years of Buddhist 
> > Studies, p. 9: “Where we find passages in which these two texts, the
> > one in Pali and other in Sanskrit, agree almost word by word, we can
> > assume that they belong to a time antedating the separation of the two
> > schools [Sthaviravādas and Mahāsāṅghikas] , which took place during
> > Asoka’s rule. ... This approach cannot, however, get us beyond 340 BCE
> > with the Sūtra texts, because their Mahāsāṅghika version is lost.” [3]
> > And Warder says “... the agreement of these two schools [Sthaviravādas
> > and Mahāsāṅghikas] should establish the oldest available textual
> > tradition ...” (in Warder, A.K. Indian Buddhism. Buddhism Series.
> > Motilal Banarsidass, 2000).


  [1]: https://ocbs.org/wp-content/uploads/2015/09/authenticity.pdf