Accuracy of various elements in circuit
A perfect op amp has infinite open-loop gain, zero input current and offset voltage, infinite bandwidth, and zero output impedance. Of course real op amps have none of those attributes, but approach them as more negative feedback is applied. 

If the open-loop gain is much higher than the closed loop gain then gain accuracy is determined by the external components in the feedback loop. Therefore 2 op amps set for low gain should be more accurate than a single op amp set for high gain.

Input offset voltage and current is mostly a function of the first op amp. The second op amp may have the same figures, but they are much smaller relative to the signal. The second op amp acts as a buffer which isolates the first op amp from load impedance variations.

Then there are practical considerations. A 10M&ohm; pot (if such a thing is available) may be less stable and harder to shield from EMI. In your circuit both op amps are inverting the signal, so the result is a non-inverted output. If that is what you want then you need two op amps anyway.