Putting it at its simplest, Jim, the bigger the battery, the more electricity there is within it. D cells are the same voltage as AAs, but that voltage will last much longer. Overall, D cells may be cheaper.
As to rechargeables, a rechargable D cell doesn't hold as much as a "disposable" one. Same with AAs. And rechargeables of any size only put out 1.2 volts each - 80% less than their disposable equivalents. That means that if your torch really wants 6 volts from 4 x 1.5V batteries, it will only get 4.8V from 4 rechargeables. The beam won't be anything like as bright. Of course, if your converter will take five 1.2V rechargeables, they will add up to 6V.
If you fancy your chances

at simple electronics, "disposable" batteries can be recharged ten times or so - see
http://madmodder.net/index.php?topic=2583.0 Andy