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I'd say a few hours will suffice, it's not that big a site.
I'd actually recommend visiting Prambanan the day before going to Borobudur, since it'll still feel impressive that way around. The best approach is to hit Prambanan in the afternoon, drive up to Borobudur, stay at the Manohara lodge on the park grounds, and use their sunrise tour package to visit Borobudur one hour before it's opened to the general public.
That said, Prambanan is on the way from Borobudur to Solo (Surakarta), so logistically it may be more straightforward to cover on your way out.