Been a Dunlop user here for almost twenty years, and never had an issue or incident of them ever coming off, with having them on over 30-35 instruments. Being a heavy duty equipment mechanic, I have always seen the design and rugged build of Dunlops to be more fool proof and far superior.
The lock buttons don't 'accidentally' push, unless you push them. But cooincidentally, over the last six years I've had to come to the rescue to four other musicians using Schallers that the nut loosened and the lock fall apart onstage (I kept a set of Schallers in my tool kit for just that reason).
If you loose or forget your strap, the Dunlop buttons are shaped like a stock strap button and work as them, so you can borrow a strap and get on with the show.
The screws are pretty big, often bigger than the stock button screws. The Schaller screws are often smaller than the stock screws.
No Loc-tite is needed to assemble them.
A snapped Dunlop screw is one in a million failure, but certainly not a 'Dunlop' failure. Could have been caused by overtightening when they were installed.
As I mentioned above, the skinnier Schaller screws would not be stronger.