They both seem to want the same thing: preservation of the fallen. However, Mithrax wants to ally with humanity. I can’t imagine Variks wants a war with humanity, though. Why do these two to-be Kells hate one another?
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1 Replysimple... [spoiler]Variks was "Loyal" to the Queen, Mithrax would have probably went to the Queen and the awoken to gain an alliance first before asking The City for peace, Variks leaving the Queen and abandoning his post would only hurt the reputation of the Eliksni by giving the Queen and the Vanguard a reason not to trust Mithrax as the most nogotiable of his race had -blam!-ed over the Dreaming City and the Vanguard with A. the death of Cayde-6 (even though it wasn't really his fault) and B. if the Variks never left the prison, then we would have never went to the Dreaming City, kill Riven, and curse the place in a never ending loop of pain and war against the Taken, Scorn, and Hive. [/spoiler]