This question most often does not even arise. It would only be valid in the cases where there is the possibility of choice. And if you remove the games that are only webplayable, because the engine offered an html5 export, it is even less.
It is two different approaches and traditions. Web games "historically" were hosted on content aggregators. Often specifically created for that purpose. Most of those were flash games. They were made to attract people to play that game on a site.
Downloadable games are a continuation of the games that were distributed on discs. People are used to having "a copy" of a game. Even if it now is fully digital distribution.
The term casual might apply here. It is lack of "commitment". Downloading something is a bit of effort, while playing a browser game is basically just opening a webpage.
You can add online features in the mix to make this more complicated.
But in the end, it just heavily depends on the game. You would rather play "Bejeweled" as a browser game or a mobile app and you would rather play "Doom", "Super Mario" and "Minecraft" as a downloadable game.
And to answer the question, it does also depend on the game. Do I believe that the advertised game is sufficiently playable in a browser? Would I want to play this game without being on my browser? It go either way.