The problem is not in calling it a split, the problem comes when trying to determine which is the true church, and which is the apostate spin-off.
The RCC and the LDS both claim unbroken authority. Which means that even if all doctrine was exactly the same, unless you were called of God and ordained and set apart by someone else in authority, then you have apostized from the true church.
In the case of Protestants they solved this by saying everyone has authority unto themselves.... which waters down authority to the point of making it meaningless.
The RLDS on the other hand claimed that Joseph Smith gave authority to his young son in a rumored father's blessing. However that still leaves a gap in authority for them from the time of Joseph Smith jr. death until Joseph Smith III finally relented and took over the RLDS. The other problem they have is that no where does it say that what they claim happened is the way authority is passed on to another. this creates an untenable position for them, as they can not claim to follow the doctrine as revealed to Joseph Smith jr. While at the same time they discard doctrine about authority and succession in order the make Joseph Smith III the leader of the Church.
In fact the their very name "Reorganised Latter Day Saints" admits to their paradox.
I have asked this question before and generally get one of two answers: "My Church is the only True Church" or "All Churches are equally true". Both answers are unsatisfactory. The first is a statement of belief. For another to accept it requires either belief or proof. For the other All Churches teach different things and if they are all equally true then they are both equally false.
It is my understanding that RLDS did not exist until Joseph Smith III became old enough and many splinters rallied under him.
The RLDS (CoC) claim authority from the Prophet Joseph Smith Jr. intending III to be his successor (from a letter, blessing, etc). The LDS claim authority from the Quorum of the 12 who have Authority as a group equal from the Prophet. Who is right is up to God to answer.
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