illustration (attribution, if any possible, is at the end of the article)
There are two reasons routinely mentioned for the (early) split between the Elders (Sthaviravada / Theravāda) and the Mahasanghikas. It is still unclear at this stage which one is the most historical.
According to the Theravāda account, the split occurred because of a wandering monk discovering a saṅgha breaching 10 vinaya rules, or so he thought. A council was then organised to debate the interpretations of the relevant vinaya rules, and the Elders considered the 10 breaches confirmed as illegal acts. The majority did not accept the ruling though, and their group split from the Elders and became the Great Assembly (maha sanghika).
Although the Theravāda account will obviously not discuss this, it is possible to assume that the majority of the saṅgha considered the orthodox position either unrealistic in the light of recent changes in context, or a form of clinging, if not an attempt to establish some person-based authority (in contradiction with the last days of the Buddha when he refused to appoint a successor).
The other version relates to a more doctrinal debate, related to Mahadeva's 5 propositions, notably reducing the status of the arahant (by making them fallible, still subject to subtle forms of temptation, of doubt and of ignorance!).
Again, the orthodox response would have been considered unsatisfactory by the majority, who would have left the Elders to their certainties.
Initially, the doctrinal differences were minor. Most of the doctrine was the same as that of the Elders. Differences amounted to the reject of the some appendices of the vinaya, of some sūtras (attributed to Sariputta, not to the Buddha himself), and of some parts of the Jātaka tales.
The departure wasn't as 'dramatic' as most people nowadays like to make it sound!
Due to the physical and doctrinal proximity, the Mahasanghikas were still very much involved in dialogues with the Abhidharmic schools, and they cross-influenced each other. There's some evidence that monasteries could even host mahasanghikas and other lineages on the same site.
By making arahants more 'human' again, the Mahasanghikas quickly reduced the gap between the lay branches and the monastic orders, keeping the fourfold saṅgha more tightly together. Lay people could thus play a part in the governmental bodies of the saṅgha, which itself led to evolution centred around the needs of the lay supporters (with a stronger focus on popular forms of practice: more devotion, less meditation… and a greater acceptance of a godly figure for the Buddha, later leading to the Trikaya doctrine) rather than the needs of the monastics.
As tales were popular, the Mahasanghika's insistence on the Bodhisattva (the to-be-Buddha) ended reshaping the ideals themselves. Not only the teachings started insisting a lot more on buddha-nature, but they also promoted the Bodhisattva ideal rather than the Arahant ideal! In turn, the emergence of Bodhisattvas also provided opportunities for more devotional practices, now that celestial beings could be called to help!
Mahasanghikas disappeared as a lineage and were close enough to Theravādins not to be Mahāyāna themselves… But a bit like rebirth, one might trace some causal relationship between Mahasanghikas and later Mahāyāna schools. The causal link isn't so much via lineages though, but via the questions the Mahasanghikas raised and some evolutions they initiated.
After a few centuries, the Mahayanists were rejecting the Abhidharmas "en bloc" and insisting of the emptiness of all dharmas though —2nd Turning of the Wheel— and the differences became starker (e.g. the "Middle Path" itself was redefined, becoming a theory of relativity instead of its initial understanding as a way of life between asceticism and indulgence).
As the focus on emptiness itself fell into an excess, the later 3rd Turning of the Wheel will introduce the Mind-Only school (to answer the question: "if everything is of the same nature, i.e. empty of essence, how comes ignorance and phenomena arise?").
It may be noted that the Mind-Only tradition, without being a return to the Abhidharmic schools, did integrate some of their conclusions, e.g. the "8th consciousness" or store-consciousness had precursors in the Abhidharmic debates over karma, rebirth, intermediate existence…
It isn't helpful or skilled to promote the competition between traditions, this is just an old habit of trying to appropriate authority, alms, etc. What's more useful is to enquire into what's shared, or how can insights be constructively combined.
photo: cave in Ellora, India © Andi Hefti (flickr.com/photos/andihefti)