An informal discussion of run time is posted here:
http://www.batteryuniversity.com/parttwo-31.htm
where you can see a number of factors involved with run time performance of different chemistries.
Vs - open circuit source voltage
Rs - internal source resistance
DoD - depth of discharge (0 - 100%)
On a per volt basis, I think the LiPO actually has greater internal resistance for a single cell.
This how you compare:
Stack up 3 NiMH Cells in a Series String:
Vs = 3*Vcell = 3*1.4 = 4.2 Volts (fully charged)
Compare to 1 LiPO:
Vs = 1*4.2 Volts (fully charged)
In this comparision the LiPO may have a little more internal resistance Rs than a stack of Sub-C NiMH cells. However the Rs in NiMH begins to rise pretty fast after 50-60% depth of discharge, and in high performance racing, this kills the peak power output from the motor, because it cuts down the amps that can be drawn when you apply full throttle. The LiPO will have a more constant Rs until maybe 80-90% depth of discharge, so you get more of the stored energy out of the pack (extended run time). These are BALLPARK figures for illustration.
If the amp draw is low in an application (not as in racing) then both batteries might provide just about the rated capacity. Amp draw is high in racing.
Now for better performance the Manufacturer (don't try this at home) can string two LiPO cells in parallel, essentially making the cell "fatter." This doubles the energy stored at 4.2{V} and cuts internal resistance Rs in half. This LiPO will substantially outperform NiMH in time delivered and peak power, without adding weight.
Power dissipated as heat in the battery is armature current squared times source resistance, Ploss = Ia^2*Rs. Since LiPO can be built with less Rs and it stays lower for a greater depth of discharge, LiPO is more powerful and more efficient.
A last minute search to confirm my logic turns up this great link:
http://www.rchobbies.org/lithium_bat...eakthrough.htm