I'm using the same Gimbal (for a Canon 7D or a BlackMagic Cinema Camera) and I'm only using a 3S 2500mAh LiPo. I have to say that I've upgraded the Yaw axis with a bigger motor (8017 i-Flight) to get some spare power. With this, I don't need to use a 4S.
Here a link to a short test video: https://copy.com/JcpDPLBDCnJD6FWa As you can see, I'm using the Gimbal Up Side Down (Camera on Top)
Only if you are using above 220 power setting with 3s. If the motor starts to get hot already with 220, no use to go to 4s. I say 220 instead of 256 because it is good to have some reserve for the voltage compensation to work if it is activated, and it is good to activate.
So confusing. There is no Magic with batteries, just understanding few things.
3S battery is fully charged 12.6 V and completely empty around 10 V. BaseCam has voltage drop compensation, for constant performance it is good to use that, see the users manual.
If you are using 3S battery and need to set the power above about 220, it is probably better to use 4S battery and lower power setting so that the voltage compensation has room to work. 4S battery voltage is about between 16.8 to 13.6 V.
The battery capacity xxxx mAh defines how long the gimbal will work, obviously higher capacity, higher running time.
RC batteries often give C rating, meaning how much current the battery can provide usually separate reading for constant consumption and short time. So is the battery is 1000 mAh 10C constant, it can provide constant 10A current and that is enough any handheld gimbal. Typically they consume less than 2A.
At 10A load 1000 mAh battery would provide power only for max. 6 minutes, with 2A load 5 times more etc.
Camera LiPo batteries might have as low as 1C rating so with them you need to use higher capacity battery, i.e 3700 mAh battery could provide constant 3.7 A current that is enough for most setups.
But it all depends of the battery and gimbal. You need to know how much the gimbal will consume current, how much the battery can supply current (must be higher than what gimbal consumes) and then you just select the capacity that gives the running time that satisfy you.
Ps. Non encoder gimbals consume constant current, Encoder gimbals consume maximum current when the gimbal is loaded, but otherwise use very minimal current and the batteries last much longer on normal use.
4S lipo battery the voltage is 16.8V(=4*4.2v) is more power than 3s lipo 12.6v(=3*4.2v), 3s VS 4s which one ? This article maybe can help you http://www.rcdronegood.com/longest-quadcopter-flight-time-3s-vs-4s-lipo-battery. Though 4s lipo battery is more weight and expensive than 3s,but there are many advantages for quadcopter as below. 1.More power 2.More payload 3.More longer SO if your gimbals can bear, 4s lipo more better. do you think so?