What, if some day or night a demon were to steal after you into your loneliest loneliness and say to you: 'This life as you now live it and have lived it, you will have to live once more and innumerable times more' ...
That, combined with a closed universe collapsing--how does it measure up? It doesn't. They are two unrelated ideas. One is more about philosophical implications, and the other about modern cosmology.
For both to be reconciled, there would have to be a perfect mechanistic materialist resurrection occurring. Although, even that is different from what Nietzsche was poking at. He did not mean one iteration of history, of our lives, continually reoccurring. He meant that given infinite possibilities, forever, every possible iteration would have to repeat itself. [Correct me if I'm wrong, but that is how I interpreted the text.] Since this life you are living now is one of such iterations, it is bound to repeat. That is the opposite of the Big Crunch.
Think of it as gas filled balloon (your life, the universe). Will it pop or be blown up the same way every time? Or superheat a rock; condense it down to magma. Then, will it expand the same way every time once cooled?
Here is a long discussion: thephilosophyforum.com/discussion/410/musings-on-the-nietzschean-concept-of-eternal-recurrence