From an application perspective, I regard them very much the same as rupture disks. If you have an application that needs a disk, but you need to ability to put the system back in service without a line-opening or temporary shutdown, then a bucking pin is something to consider.
I've seen them used in vent collection systems, to allow emergency excess pressure from System-A to be diverted to System-B. In applications like that, normal control valves are not sufficently reliable, and relief valves are impractical due to the large size requirement. A common rupture disk would work, but that requires a major outage to re-install a new disk. Bucking pin devices are ideal for this type application because they can be closed and put back in service without any plant interruption.
That's an example of a good fit for a buckling pin device. I'm sure there are others, but I haven't come across one. Personally, I have a huge bias against all non-reclosing devices. They cause more plant problems and hazards (personnel and environmental) than any other type relief device. There are some particular applications where they're needed, but they're few. I'd never use any non-reclosing device in an application in which a PSV was suitable and practical.