Scenario 1 (QR code) puts 100% of the infrastructure on the client (visitor) side, and scenario 2 (Nest, Ring, etc) puts 100% of the infrastructure on the server (resident) side. [Edit: strained metaphor perhaps, and yes both scenarios require connectivity infrastructure]
So these are completely different methods of achieving the same goal, and there are easily imaginable cases where one scenario would be preferable over the other.
Usually, server-side makes the most sense. Certainly in the case of a traditional wired or wireless dumb doorbell, it's simpler.
But there are cases where server-side is difficult or impossible, especially if you want "smart" features like photos or routing or two-way interaction. Higher cost, permission from property owner if renting, etc.
Pushing the infrastructure to client-side solves these problems. Most users will have the client infrastructure in their pocket already. No wires. No new piece of hardware to maintain, repair, keep charged, etc.