The 625 is a faster servo, but the 645 has more torque. For your buggy I would use both 645's for steering and throttle. You'll have stronger brakes and no problem turning those wheels.
You got it right on the batteries. All that a Rx does is gather the signal sent by the radio, while the radio actually transmits signals, hence needing more power.
Are you having problems with distance on your model?
TTYL, Gary