Bias instability in Gyroscopes : AVER / ADEV
According to this app note by Freescale: http://cache.freescale.com/files/sensors/doc/app_note/AN5087.pdf

which came from this recent related question: How to interpret Allan Deviation plot for gyroscope?

with a copied graphic below where they give the bias instability for each axis.  What a specific manufacturer does on their datasheet, you would be best asking them directly. 

Yes you would want to see a low bias instability, and I would think that the same number at a lower $\tau$ would actually be worst unless you were only concerned with doing a measurement over that short duration in time (implying the turn-up occurs sooner so that unit would then be drifting sooner and over the longer duration would be a lot worst). You ultimately want the lowest value at the further averaging time indicating the best long term stability, but depending on the process and use, there may be reasons to be concerned with shorter term stability as well such as if you were making difference reading measurements at 1 second intervals (then the 1 sec ADEV would be of interest).