To determine the run time, you will need to look at the amp hours (or miliamp hours) of both configurations AT THE AMPS that you will be drawing. Factor in the voltage and you will have watt-hours.
Once you have watt hours, you can pretty much tell which will run longer.
The gotcha is that some converters are more efficient when the voltage closely matches the output. They more or less burn off the difference in voltage. The TLE300m purportedly uses a DC-DC converter, and per batteryjunction.com it uses 12 watts. That's 2 amps from a 6 volt battery pack.
A typical 9AA -> 3D battery pack will give you 4.5 volts at 6,000 mah. That's assuming 3 cells at 1.2volt in parallel wired in series with two other 3 cell modules.
A typical 6V 5X1/2D NiMH pack will give about 3,500 mah.
Using these numbers, the AA system will deliver 27 watt hours where the 1/2D pack will deliver only 21.
BTW, The battery junction web page says that the TLE300m really needs 6 volts. That limits your choices.
Daniel