It's true, the HTTP API documentation for the package manager went missing in one of the latest versions of the product documentation. Can you raise a Daycare ticket for it and ask to make it available again?
Regarding OSGI installer ("install" folder) vs package manager: From a reliability point of view they are the same; the only limitation is that you cannot deploy OSGI bundles via package manager, but you need to wrap them into packages. But internally both use the OSGI installer to start the bundles.
But I still prefer the package manager, because it's quite easy to make your AEM unusable with the install folder:
* copy a bundle into the install folder
* wait till it is installed
* shutdown the AEM instance
* remove that file from the install folder
* startup AEM again
(ok, this isn't a problem when you just use content packages.)
On the other hand side the package manager HTTP API is a bit problematic, because just uploading and installing packages in a row does not always work, and you need to handle the error detection, retries etc. Doable but the many trivial "automation scripts" you find in the internet only focus on the happy path. Might work in 90% of all cases.