Yeah, the FFXIII dreadnoughts indeed did look a lot like the Sweepers from FFVII, but their appearance in ARR is most likely just another example of cross-game fanservice, like FFVI magitek armour or Cid's airship being called the Enterprise.

Hydaelyn is not Gran Pulse or any other FF world/universe (after all, some people have also said it's Ivalice, FFVII's Planet, FFIII's world and others simply based on similar references), its it's own separate world and universe.