Quickly googling, the xbox 360 controller takes two AA cells. That pack on DX is "nimh", and the dimensions are approximately that of two AA cells wrapped in plastic case (well, 4mm extra thickness). What the manufacturer probably has done is put two 2400mAh AA cells inside and called it 4800mAh, but we're not that easy to fool.

Two 2400mAh AA cells are 5.76 Watthours. A BL-5J is 4.88 WattHours. On top of that you'd have to run a boost converter to bring the voltage up from 2.4 to 4.2 or 5V, which probably loses about 30%, so then you're down to about 4Wh, or about 80% of the original BL-5J's energy...