Absolute comparisons like 'Founder of Haute Horlogy' make no sense - both companies are more than 150 years old which gives us sufficient time horizon to compare. Royal families bought both Patek, Vacheron, and many other brands. For some people appreciation of a person that was born to privilege acts as a detractor not a positive.
Both Vacheron and Patek competed via e.g. Packard and Graves to develop more and more complicated watches, however in the end it was Patek that was victorious (I think we can assume money on both sides was not an issue) - the very fact that Vacheron waited more than 80 years with the use of CAD and modern manufacturing techniques to design a watch more complicated than the Supercomplication speaks to technical competence of Patek.
Then there are recent developments including Fifty-Six collection carrying 'Richemont group movements' - some people will not mind and welcome this development aimed at bringing a new segment into the fine watchmaking family, however you cannot deny the fact many will consider it a loss of prestige.
In the end there are no things such as 'most prestigious watch company' or 'best watch' since one has to start by figuring out how to compare them, and a common set of criteria is impossible.