I've got both. About 24 of the Tenergy 10,000 mA/hr Ds and 6 of the Accu Power "Evolution" LSD NiMh D cells that I got from Thomas Distributer. I am getting the impression that the Tenergy's are far from 10,000 mA/Hr, perhaps half that, so I have a set of four "conditioning" on my Maha 808 charger. The "Evolution" LSD cells are awesome, I am using them out of the package straight into a boom box that I use several times a week and its holding up better then the Tenergy's or any Alkalines.
I've heard they're closer to 8000mAH, but a spongy design that is only reasonable at low current like under 4A.
Because of the costs, I may consider NiCds especially in LED lantern applications which I originally bought the Tenergy D NiMh cells for, for emergency blackouts and for my D-Cell maglites. The reason is that the LED lanterns can be left on with NiCd until fully drained. I noticed that the Tenergy's if left too long dropped well below 0.9 volts which will damage the NiMh cells. NiCd would actually benefit from getting drained all the way and they have lower self-discharge...about half of a NiMh.
Eeek! Your lantern cannot be left on any longer (lower drained state) with NiCd. NiMH don't have a lesser drain threshold and NiCd cells do reverse charge (-> damage) when the weakest hits 0V but the rest aren't and pack still supplies power.
No NiMH will be damaged if drained below 0.9V. What will happen with those, as with NiCd, is if the cells aren't perfectly matched in capacity (or as they age, there becomes a variation in capacity later), that by the time some cells have hit 0.9V, other cells in the series will have come far closer to 0V. If you were able to monitor every cell and immediately cut out the battery pack the moment the weakest cell got to 0V, your cells would be fine.
NiCd do not benefit from being drained all the way. That just makes it more likely that one in the series would be reversed. In rare uses when they were overcharged, in that case draining them close to, but not totally drained, would help to prevent voltage depression (not to be confused with the mythical "memory effect" which is almost never seen in real-world uses). However, in any device where the battery pack voltage is boosted, such as in a typical fluorescent lantern which converts the pack voltage to hundreds or more volts to drive the tube, voltage depression on the NiMH or NiCd pack will not be a problem. By draining them fully you wouldn't gain anything useful unless the pack was a cell or two short of needed threshold voltage.
In other words, suppose your lantern regulator board can't drive the tube if the pack voltage dropped below 4.0V. If that were the case, and the pack were voltage depressed, then you wouldn't get full spec'd capacity out of a 4 cell pack. On the other hand, if minimal regulator board voltage input were 4.0V but you had a 5 or more cell pack, it would be no problem.
With an LED instead of fluorescent, it depends on whether it has a current limiting (simple resistor, typically) or boost or buck LED driver circuit. With current limiting it would work but be lower light output. With boost circuit it would work similarly fine as with fluorescent. With buck it could potentially drop lower than the threshold for the driver circuit too soon (same issue as with fluorescent, depends on # of cells and exact threshold for driver circuit and LED config - whether one, or more in series or parallel to determine minimal forward voltage drop plus driver board drop as a total to compare against remaining battery pack voltage if/when depressed). Even with depressed cells, you still get the capacity by the time the pack is down to a normal shutoff range of under 0.9V.
There's really less difficulty in choosing NiCd or NiMH. The former has almost double the recharge cycles and works better at low temps. The latter has more energy density and isn't as toxic. Some say NiCD can be recharged faster, but that's generally only comparing when the NiCd has a lower capacity so in the same time period a good quality NiMH can have the same power put into it until talking about extremely short, very high current charge rate periods like under 20 minutes.