Alway remember that electricity is lazy...it will only put out the minimum it takes to get the job done.....if you hook a power source that is capable of delivering 1000 amps to your airplane, transmitter, or anything in our hobby..and turn it on your only going to draw the amount of miliamps it takes......Now change the voltage from 4.8 or 6 volts to say 9.6 volts and you're going to see the magic smoke that makes things work...once you let out the magic smoke its ruined.....bottom line as long as your battery has more capacity than the load requires and the voltage is the same you're ok.
Downside to bigger mAh batteries is they take longer to charge.