I would say that the eagle rescue is definitely eucatastrophic; after all, in On fairy stories, Tolkien states (in refference to this):
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But the 'consolation' of fairy-tales has another aspect than the imaginative satisfaction of ancient desires. Far more important is the Consolation of the Happy Ending. Almost I would venture to assert that all complete fairy-stories must have it.
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moreover, in a 1944 letter to his son, he reffers to the eucatastrophic emotion felt by Bilbo when is saved by the eagles (the "sudden joyous turn") - so I would say both stories "end" in a rather similar fashion.