What happens if William II of the Netherlands is killed at Waterloo?
The Netherlands has one less incompetent king. Sorry, I am not a big fan of Willem II, even though he is the one responsible for the Dutch democracy. But I believe that was just a symptom of his incompetence.
Anyway, the biggest difference at first would be during the Belgian revolt. His actions there basicly made a tense situation worse. Without him I could see a compromise happening in which some federation was formed. With him in Brussels the Belgians decided to make a constitution that said that noone from the house of Orange-Nassau could become king of Belgium.
The second difference would be the Dutch liberal constitution. Would his brother accept a liberal constitution for the Netherlands? I don't know his character that well. The thing is that if he doesn't the monarchy in the Netherlands might be in danger, especialy if Belgium is still part of the Netherlands. Personaly I think he will, although maybe a more watered-down constitution, less liberal, more conservative with more power or influence for the king.
Another difference is no king Gorilla (Willem III). That can only be a good thing.
Last difference, a possible continuation of the personal union of the Netherlands and Luxemburg. It is hardly certain as Frederik had no surviving sons, but the POD is before his and his brother's marriage, so I think those children will be butterflied away. Frederik will probably marry Anna Paulowna, like his brother did OTL.
BTW Frederik will still be known as king Willem II, not king Frederik I.