In the case of PagerDuty, my
exceptionally strong preference is for a physical pager, which is passed, fully charged, to the next person on call.
If the person passing off the pager hasn't charged it, they hold the pager until it is.
Why?
Because if I don't have the pager, I know I don't have shit to worry about. I swear to the gods, that literally nearly killed me. The psychological pressure, over years, of being on-call or 2nd on call (small teams suck) bears down. The moreso with technical debt, buggy sites, and verbal lore recovery methods (trust me, I document the motherloving hell out of everything, but there are bits that are buried very, very deep).
If you're contracting services or running your own sites, a separate pager still offers benefits. Again, it can be handed off, and you know when it goes off there's trouble (yes, you can also program different ring/dial tones, etc.). I'm also impressed by the robustness, range, and battery life of physical pagers, another benefit.