I think Rhalgr and Ramuh would end up being vastly different since we know from Koji Fox himself that if two groups summon the same primal but have different interpretations how that primal actually IS we could, theoretically, have two different primals sharing a name and a similar appearance but still be different (plus, they would be summoned at the same time, if my memory serves right). Rhalgr could be similar to Ramuh but I highly doubt we'd wind up with Ramuh if the Resistance succeeds in summoning the Destroyer.