In days not so distant past, Alkalines would outstrip re-chargeables on their ability to deliver high current for short periods (Note this is different to mAh rating). So taking an Alkaline and a NiCad or NiMh battery, the Alkaline would win on max juice supply for short periods.
Things have moved on. Now NiMH is better than Alkaline and NiCad on capacity for size and peak current. However, most advances have been in the popular AA size. I'm not so sure about the less popular AAA's.
As sjms says, self discharge is the drawback of re-chargeables. Whereas Alkaline and Lithium are fine in clocks radios and calculators that get intermittent use. If you don't mind re-charging your AAA's every few months, they might suit you. BUT you can buy 2 sets, 1 with charger, and keep that set plugged in all the time. Make sure the charger is designed to take AAA cells and choose a 4-6 hour one rather than a fast charger.