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1AOne battery has 400 mAh more, and this affects both how long it will last and the amp output.
Amp output assuming it is a 1C battery then:
4400/1000 = Ah 4.4 (this is to convert mAh to Ah)
4800/1000 = 4.8 Ah
and C*Ah= Amp Output so the numbers remain unchanged and the bigger battery will output 400 mA (.4A) more current
as for how much longer the other will last:
4.4 Ah at 4 amp draw the bigger battery would (theoretically, but voltage drop between the two batteries may make this false) last 6 minutes longer.