1. The Ring doorbell costs less. In my country, £89 for a basic Ring vs £203 for a basic Axis webcam.
2. The Ring is battery powered, which is only possible because it doesn't have to run its radio and CPU all the time in order to be a web server. Being battery-powered makes allows self-installation by a much wider audience.
3. If someone steals your webcam with microsd recording, they steal the video of themselves doing it at the same time; with the Ring that is not the case.
4. IoT devices are famously insecure, and network webcams famous for being inadvertently made public. The Ring doorbell doesn't need you to open a port in your firewall (exposing it to the public internet) to be remotely monitored.
With that said, personally I still wouldn't buy a Ring doorbell.
I also would never use the ring doorbell. Not only is that a security risk, but it also provides eyes on neighbors across the street. Legal, sure, but dodgy.
If you are viewing it while not physically present it must be uploaded somewhere - otherwise it couldn't be on your phone right ?
On notification you could choose whether or not to record the stream and save it as a file on the client.
Said service could provide a guarantee that all data passing through its servers will not be recorded, persisted or even decrypted.
One of the neighbours has an 12 camera setup with a NVR. They just took the NVR.