Likely, the long-term outcome would be the same. Harald wouldn't have been in a great position to fight of William, either. He might have simply ceded southern England without even a fight.
And given William's subsequent Harrying of the North, I don't think that Harald would be able to hold on to it very long. He was intent on taking over the whole thing, and he had a much stronger force coming over the English Channel than over the North Sea.
Of course we can never really tell. I could spin a million other possible outcomes. But in this case, William really did have an overwhelming force. Godwinson had a home-field advantage, and might have won if he hadn't exhausted his force just getting there. The Vikings weren't going to fare better.
Counterfactuals abound in this. What if Stamford Bridge had failed?
What if Harold had won?
Likely, the long-term outcome would be the same. Harald wouldn't have been in a great position to fight of William, either. He might have simply ceded southern England without even a fight.
And given William's subsequent Harrying of the North, I don't think that Harald would be able to hold on to it very long. He was intent on taking over the whole thing, and he had a much stronger force coming over the English Channel than over the North Sea.
Of course we can never really tell. I could spin a million other possible outcomes. But in this case, William really did have an overwhelming force. Godwinson had a home-field advantage, and might have won if he hadn't exhausted his force just getting there. The Vikings weren't going to fare better.