Their relationship was stretched and then ultimately destroyed over the course of Dawn Of The Planet Of The Apes, as Koba shot Caesar before Caesar then killed his old pal, despite Koba’s pleas not to do so, as he insisted that apes do not kill apes.
Because of the huge weight that Koba’s death clearly plays on Caesar during War For The Planet Of The Apes, it seems unlikely to me that Matt Reeves would simply reuse footage from Dawn Of The Planet Of The Apes to underline their friendship.
Caesar rejected this notion and then threw him off the top of a tower, which was understandable.