Can't say anything about the others, but I don't think a single Knights of Sidonia mech could take down anything more than a few dozen Cabal ships... Especially when you consider that before the protagonist shows up, humanity had never defeated the... Alien enemy that I forget the name of.
Edit: The Autumn might not be able to solo 1000 either. Still could give a pretty good fight for the odds.
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I would use his mech, but it would be one of those where your out numbered. It would be good because of its agility but not good enough for 1000 enemy ships.
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As I said, likely a few dozen then toast. And even then, wasn't his mech used by others before to less effectiveness? It was an old model, but I don't believe it was the only one made. Could be remembering wrong, though.
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It was older however he could use to great success due to all the flight simulation training he had done. Now if we had say 1000 of these with great pilots then it would be even. I would even say maybe each pilot could take 5 enemy ships each. But again it depends on the pilot.