If Harold (Godwinson) faces William before Harold has to deal with Harald, William is in DEEP trouble. Hastings was a near run thing IOTL. If Harold has his Huscarls at full strength, his fyrd at full strength, and all his forces are relatively well rested (NOT just having rushed South after a battle), the odds change strong in Harold's favor. I think he'll defeat William pretty soundly and force him to withdraw.
William and his remaining forces can then play for time and either pull back toward his ships or choose some defensible terrain and try to force Harold to attack him. In either case, his situation is improved when Harold gets work that Hardrada has landed up North.
In this situation, Harold probably leaves a holding/harassing force to either hold William in place or force him to flee by ship. He takes the core of his force up North to face Hardrada, but he probably takes more time.
Depending on what forces he's able to bring North, he may not attack Hardrada immediately -- he may wait to build up strength and/or resolve the situation with William. He could be faced with having to split his forces and having two enemies where can't afford to attack either one.
Ultimately, I think William will have to withdraw -- his forces are bloodied, supplies are thin, they're in unfriendly territory, and William and his knights have to worry about issues back in Normandy (including lands of fellow lords/knights that fell at Hastings).
With William gone, Harold can marshall enough forces to crush Hardrada.
So, ultimately this is better for Harold, but not as good as if William had landed back in Jun/Jul as he wanted to. Had William landed in July, he would have been crushed. His fleet would have been attacked/harried by the Saxon fleet before landing. Then, his somewhat weakened force would have met Harold at full strength. Once he loses, his survivors are going to be harrassed as they get to their ships and then again once they're at sea. Meanwhile, Harold would have time to build back up before Harald Hardrada appears.
What if Harald Hardråde (Hard-Ruler) lands outside of York on the 15th of October 1066, a day after the battle of Hastings? How would history go if that happened? Who would have won the battle of Hastings, as Harald Godwinson's army, even though they won at Stamford Bridge, was depleted and tired after the fighting at stamford bridge. And of course there is the forced march from the south up to the north and then down south again to meet William.