Due to high common mode voltage of input signal, I want to stage AD620 with ADS1115 for building a signal conditioning unit. Theoretically there are multiple ways to set gain for AD620 and ADS1115 for a given resolution in final output. Two such cases are given in the figure. Practically, what will be the best setting among these two if we consider other performance parameters ? (Eg: low noise in the final output)

 

Generally you want the first stage to have a significant gain (e.g. >10) so that the any noise from the first stage dominates and the noise from the second stage doesn't add appreciably to the total.
Beyond that it likely doesn't make much difference how you divvy up the gain.