Gonzo,
I am no EE person either, but only have some experience with different boards popularly used for driving the lux.
Given it is a constant current boost or buck board, the regulated runtime for TxxH will be longer than the TxxJ, but the brightness will basically be the same since they are both under the same lumen category (T) and current is the same.
For ex, a BBNG(constant current boost board) with TW0J and TW0H, they will have approximately the same brightness, but TxxH generally will have approximately 15-20 minutes longer runtime than the TxxJ(from my experience).
Another ex will be the Downboy(constant current buck board), it will go into DD mode once the battery voltage is the same as the lux Vf. So naturally, it will take longer time to drain the battery to the lower Vf of TxxH than the TxxJ.
Hope this helps.