I suspect that the difference would have been that Hardrada would not have been a position to attempt to stub out the threat from William at Hastings, so that battle wouldn't have happened and the ensuing campaign would have been quite different. William benefitted hugely from the lack of any resistance figurehead, whether Hardrada could have provided that is unclear. Different magnates are likely to have backed different horses, some declaring for William, and some for Hardrada, with the war between the two perhaps also leaving an opening for an actual English leader. William was a chillingly effective conqueror, but Hardrada was a hugley experienced and successful campaigner. Who would have won out, who can say? But certainly Hardrada's could have been expected to have been more of a continuity regime.