How to convert noise to noise density in mic pre amps
TI is quoting a spec based on the total noise in the audio range (20 Hz-20 kHz, presumably), adjusted based on a standard A-weighting curve (see http://en.wikipedia.org/wiki/A-weighting for more, as well as figure 22 of the TI data sheet.)  -89 dBv is what you'd see if you looked at the noise on a scope, after passing it through a filter with that particular response. Something on the order of 30 microvolts.

To compare that value to the MAX9814's specification, you can multiply 30 nV/root-Hz by sqrt(20 kHz-20 Hz) to get 4.3 microvolts of total noise in the audio spectrum.  

This is all complicated by the fact that the volts-per-root-Hz concept assumes constant noise power per 1 Hz of bandwidth.  This will not apply at offsets near DC where the noise takes on a 1/f characteristic, and neither manufacturer gives explicit information about their part's 1/f corner frequency.  With these two chips in particular, you need to compare them via the one spec they both provide: the A-weighted SNR (60 dB for the TI part, 64 for Maxim.)