Voltage reference with op-amp buffer and additional filtering
I don't know why the designer did that. There may be a reason. I'd
  like to understand under what criteria the designer would choose this
  topology.


Op-amps generally can't handle excessive capacitance on their outputs such as C2 and C3 in your 2nd circuit and so, if the designer feels he or she needs to add them for extra noise immunity on the Vcc/2 line then, precautions need to be made to ensure that the op-amp does not turn into an oscillator. Those precautions are C1, R3 and R4.