See the Update below.
Nowhere in your post do you say what your accuracy and stability requirements are, or anything about power budget, cost budget, output current, noise bandwidth, etc.; so all of this is guesswork.
The first circuit will not work; the opamp output shorted (through R12 and R13) to what I think is a GND symbol drawn incorrectly. Also, low voltage zener diodes are not nearly as stable as 6.2 V - 6.8 V parts. But no zener diode can compete with a high-accuracy and high-stability reference IC from National Semi, Analog Devices, Linear Tech, or Maxim. Yes, I know some of those companies have been bought and sold, but the old names are better.
In terms of accuracy and stability, the second circuit is much worse. It depends on the performance of two different voltage regulators, neither of which is designed for reference duty, plus the thermal performance of three resistors. Compared to an old, cheap LM4040, its output will wander around every time the door opens or someone walks by.
I would start with the first circuit, go with only one reference diode, and (if you really need a bipolar output voltage range) a different opamp circuit with gain that ranges from +1 to -1 with a single pot.
Here is a schematic from an old issue of Electronic Design for an opamp circuit that goes from positive to negative gain with a single pot adjustment. For your application, ignore the A2 circuit
The gain of the A1 stage goes from +0.5 to -0.5. With a 4.096 V reference IC, the output will swing from +2 V to - 2 V. Note that the source impedance at V1 must be zero ohms, or very low relative to the other resistor values. And, of course, use something other than a 741.
You still have not told us the output voltage range you need, so, again, this is mere speculation.