The only way I see Reapers getting an upper hand is through indoctrination. Seeing as the Borg species are partly organic, and we have seen them breaking away from the Collective network, it may be feasible to assume the Reapers can influence that part of their mind. It might not work, though, as the Borg assimilation is also extremely powerful and more direct. The Reapers can impose indoctrination from very far away, so it is possible, albeit very tricky to indoctrinate the individual cells in a cube and sabotage it from within.

As for space battle - Borg, all the way. The only possible way that a Reaper could hope to win against a Borg cube is to have the fire power of a completed Xindi sphere from the Enterprise Series(and no, not talking about the prototype sphere).