The 1.2V NiMH cells have a lower initial voltage, but a flatter discharge curve. For the 4x1.5V AA setup this means the servos will run slower at full charge compared with 4xAA Alkaline, but the voltage will be more consistent throughout the run and the servo won't slow down as quickly as with the Alkaline. Out of these two AA options I'd definitely pick NiMH.

The 5 cell pack will have the same discharge characteristics but the extra cell means the voltage will be higher throughout the run and you'll be closer to 6.0v. Out of all the options you've mentioned, this is the best.

https://www.powerstream.com/AA-tests.htm