Why would you send mobile FB clicks to your website? Send them to a mobile app on mobile (!!!)
You can target only desktop users, if you want to send people to a website
You can target only desktop users, if you want to send people to a website
I don't know a single user who enjoy being sent to a mobile app instead of the website.
If being hated by your users is not enough of a deterrent, then factor in the cost of building said apps on mobile platforms and maintaining them through time and new smartphones versions while having a website versus simply having a website.
Unless you're a big corp with tons of money to throw out the windows, the wise path is a well thought and designed website.
I don't see why you would be hated by your users? The ad makes it super clear that it's an app, it takes you straight to the app store where you can read reviews / description / screenshots and then you just install it.
I think you are making the mistake of thinking that the average user is like you, most people will just want to get the app ASAP when they see an ad for something that seems useful; not having to navigate a website which doesn't have a mobile version (try budgetsimple.com in an android phone, it's impossible to use !)
Do people really install random apps because they saw a one-sentence advertisement on facebook? I really don't know what normal behavior is for the average facebook user.