Why use two power sources when designing a voltage regulator using a zener diode
The only thing the extra power supply is attached to is the negative rail of the op-amp. This would allow the op-amp to have a much greater voltage output range. If you're near the negative voltage rail of the op-amp in the first circuit, it's possible you'd start clipping. This situation could occur if you're trying to get a very low output voltage from the voltage regulator.

In summary, if your first circuit allows you to go from 1-11 volts regulation, then your second circuit would allow you to got to 0-11 volts of regulation.

The added power supply is somewhat unnecessary if you're not using the regulator near the bottom rail or if you use a rail-to-rail op-amp instead.