Even back when Apple provided a dedicated version of OS X as the Server operating system e.g. Snow Leopard Server it was not actually that different to the client operating system. The client version of the operating system had all the same server components like Apache installed as well it was more that the settings and sometimes locations and versions of those components where different.
So the current situation with Server.app is that it installs extra settings to turn on those components and provides a very easy to use interface for configuring them. Once again things like Apache, Bind, bootpd, etc. are already there on standard OS X.
So the answers to your questions are -
- Yes features have been lost
- No Server.app itself does not make things more unstable, in fact once you have set things up just like the old days you do not have to have Server.app running all the time and you don't even have to have the computer logged in as a user
- No OS X Server is not a viable Enterprise solution, but neither was Snow Leopard Server really, this is more down to the limited functionality and the almost complete lack of ability to create fail-over or clustering configurations, etc. however look at the price, you are not being charged Enterprise level costs
Where some functionality has been lost in Server.app vs. Server Admin, some of this can still be done manually via the command line, for example installing MySQL, configuring FreeRADIUS, etc.
In particular Apple's own VPN server module is still present but is from an Enterprise point of view extremely dated technology not fit for Enterprise use - it cannot even do VPN-on-Demand for use with Apple's own iPhones!