No thanks. Not keen on either. A more interesting scenario would be that Sir Andrew Moray didn't die but Wallace did...... keep Margaret Maid of Norway alive long enough to marry Edward II and unify England and Scotland in the 1300's or stop the American Revolution and create a federal United Kingdom of Britain, Ireland and America.
One thing to change? I'd make sure the Big Bang doesn't happen.
If I can't do that I would kill Karl Marx. Nothing wrong against what he says, but rather the way some people take it (North Korea, Mao, Stalin)
Maybe have the English Fleet in the Solent upwind of William's transports and cause critical losses. Or William gets killed (he nearly was) or Gyrth and Leofwine fight Senlac whilst Harold waits in London for the Cheshire and Gloucester levies, then comes down and sweeps up the pieces.
It's interesting to read all this talk of Harold Godwinson. I know a guy who claims to be descended from him (He has yet to prove it).