Taking a crude stab at it, the TI (Nat Semi) LMV1012 has four fixed gain configurations. The highest gain (24dB) one is likely to be the quietest (by analogy with other low noise amp designs) : its output noise level is specced at -82 dBV.
Thus its noise referred to input level is:
N(in) = N(out) / Gain
= -82 dB - 24dB
= -106 dBV
= 5 uV.
(Re-running for the lowest gain configuration shows it to be 2dB noisier)
Converting to a noise density (voltage/rtHz) requires some assumption about the bandwidth : I'll use sqrt(20000) = 141 which is WRONG because the noise measurements are "A weighted" (which makes them look better on paper). Finding an appropriate conversion for A-weighting would improve the calculation : HOWEVER:
5 uV / 141 is about 35 nV/rtHz, which is broadly similar to the other part.
Both are a long way from the better-than-1 nV/rtHz of a good low noise mic amp, but probably adequate for a cheap electret microphone.
So I see no compelling reason here to choose one over the other : other considerations like cost or power may help.