How does the capacity of a Duracell-brand AA cell (Duracell ordinary
or Duracell ultra) compare to one of the high-capacity NiMH cells (eg
2100 mAh)?

It depends on current drain. Alkalines are vastly superior in low drain
appliances, such as clocks or smoke alarms, to the point where NiMH would be
useless. In high drain appliances, such as DVD players with integral
screens, the alkaline would be in chocolate teapot territory.

The changeover point where one is better than the other is very much in the
direction of low drain. Any appliance that uses remotely much electricity
will much prefer NiMH, even with the lower nominal voltage. In fact, the
alkaline will produce a lower voltage for most of its discharge cycle in any
medium to high usage application. 1.5V is only available when the battery is
totally fresh and not being discharged to any extent. Any depletion in the
cell, or any current drain will result in rapid voltage drop, often even to
0.8V or so. This doesn't happen with NiMH. They can produce almost full
voltage until very nearly depleted, even at high current levels.

Christian.