It was not a matter of conflict, as Prophet PBUH never told that what type of Government will be formed after his carnal demise? Whether it would be a Democracy, Autocracy, Kingdom or Caliphate. But yes, it was clearly present that whosoever will take the reins of Muslims will take decisions as per merit and will have a "Shura" or a Consultative body on the basis of which decisions will be made. An Islamic state or a state with Muslims as it's rulers will take care about all the matters in the light of Quran and Sunnah of Prophet PBUH.
It is very baffling that basically Quran was the binding power of all Muslims at that time because the proper compilation of all Hadith (sayings) of Prophet PBUH was not present at the time.
All the tales and stories which we read about the conflicts between the Companions of Prophet PBUH and the family of Prophet PBUH are not such they weigh more for Muslims of present era to lead a life pleasing to God and getting paradise in the end. All the stories about the conflicts are highly vague and mostly based on the historical books which are highly unauthentic. Muslims after thousands of years are not getting a complete authentic picture of conflicts which are the bases of all this Shia-Sunni Conflict. As far as the Authentic Books of Sunnis are concerned, they both hail the family of Prophet PBUH and Companions of Prophet PBUH, although there are some accounts mentioning the conflicts but not enough to make someone believe that the friends and family of Prophet PBUH hated to such extent that they actually lead to the major division of Muslims.
It was all political in nature but Muslims inherited religious bigotry in terms of sects,instead. Those who exploited historians at that time fulfilled their political motives and the common Muslims stand belligerent with each other, after that.
As far as the Authentic books of Shias are concerned, they don't give their books that level of authenticity which Sunnis give to their six authentic books. How Shias give so vague accounts a reason to develop hatred for people following other part of Islam, thousand years after?
Does it really hold ground that unauthentic history and vague traditions are enough for mankind to kill each other? Muslims are clearly told to be united on the bases of Quran first which is not vague, which is most authentic and followed by all Imams whether that of Sunnis or Shias.
After hundreds of years, who knows what the reality of conflict was? Most of the companions and family of Prophet PBUH intermarried their children with each other even at that time. How the cut-throat rivalry was even possible?
Therefore,it will be wise for all Muslims of present era for the good of both this world and after-life that they stand unite on Quran as this is the actual litmus test for one to be a Muslim or non-Muslim and leave rest of the ambiguities of History to their God to forgive if we have a just or bad stance on the bases of that history.