I have noticed that in Christmas Eve On Sesame Street, in most of the scenes where Big Bird and Oscar interracted, that when Big Bird speaks, we see a wide shot of both characters, but when Oscar speaks, the scene usually just cut to a close-up shot of oscar, so Caroll Spinney probably switched over to performing oscar in those scenes. I do know that there was at least one wide shot where oscar speaks and no scene cutting was done.
Big Bird and Oscar were also seen together in 4030 1/2(SS4DMM). But it was Matt Vogel who was performing the bird, and I dont know if Caroll was doing Oscar, but I read somewhere that John Tartaglia performed him.