Based on The General's like two appearances, and what I know about Destroyer, I think either stalemate or Destroyer BFRs General. If Destroyer's mobility isn't great, it would be possible for General to BFR Destroyer too. I don't think either could put the other down with pure power.
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the general doesn't win this and there's no real reason to suspect he could handle the disintegrator. even finger blasts have carved wounds in thor's hammer. general is a tough herald. he's not beating the destroyer even 1/10.