I would say neither, as with all wars, single battles do not determine the course of events but rather the larger series of events that contribute to the singular and dramatic downfall. For the Waterloo campaign, it was Marshal Grouchy.

Marshal Grouchy was a newly minted and rather inexperienced full force commander but a skilled cavalry commander. As such, he had little experience in the movement and command of large, complex, and slow moving forces that a corps commander would be involved with. So, there is some inexperience that leads to the ultimate problem, Grouchy wasnt st Waterloo.

Days before, the French under Napoleon had defeated Blucher and his Prussian army at Ligny. To harass and defeat the survivors, Napoleon appointed Grouchy and his Corps to pin Blucher so Napoleon could defeat Wellington in peace. However, the morning of Waterloo, Grouchy was stuck attacking a rear guard action that fooled him into thinking that the full army was there, thus Grouchy contributed very little to the campaign itself.

Other small things contribute to the winning of the war, such as the poor work done by Marshal Soult (replacing the irreplaceable Berthier whom died months earlier from a suicide) as Chief of Staff, placing the irreplaceable Marshal Davout as Minister of War (however there are few that could take that role, Davout was the only Marshal that returned to Napoleon that could serve in every capacity with unusual efficiency), and the odd choice that Napoleon made to attack Wellington at Waterloo (ground that Wellington had chosen rather than ground Napoleon forced Wellington towards.)

The Waterloo campaign is probably one of the most famous campaigns in world history, but looking deeper at it will reveal a tired and ineffective Napoleon that just wanted to rest.

Your question is strange because it begins with the premise that one of these buildings was "significant in winning the war for the coalition"; the Battle of Waterloo was significant in winning the war - not particular areas of the battlefield.

La Haye Sainte fell eventually, Hougoumont didn't. Both were key positions in Wellington's line but the two farms were just part of a much larger battlefield which contained numerous other geographical features (e.g. Placenoit, Wellington's reverse slope, the sunken lane and the hedges that lined it etc etc).