they both will be using a direct drive, the one using a 6V DD and the other using a 4.5v DD
so drive TIME wont have much to do with drive power. the lithiums will run for many hours, like 30+ in a row, BUT due to the small size of the cell, will be limited in output current (as you well know)
A76s AG13 type cells are weak little cells, even primo brand name versions of them start out high punching up some good power, then quickly dwindling down in output, then if you rest them , they will punch up again.
the 2x 2016 will actually overdrive a led at first, the nichita being able to handle it a bit more than other cheap leds.
the alkaline will not overdrive the led as hard, and if its left on, it will dwindle down in output much faster. the led itself is less likly to become "ruined" lowered in output on the alkalines, over long times, you can see this with cheap china leds in them going badly, and in people who update the LED with ANYTHING see huge increases in output, because the other led was getting toasted.
so , doing any MATH on it would be very difficult, its 2 completly different worlds. and they BOTH will have very long output dwindling down lower and lower. with the alkaline wanting more rest periods, than the lithium. the alkaline treating the led better.
so
if a runtime was continuous the lithium would win easily, but keylights are not run like that usually, usually the use of them is sporatic.
so if you wanted a Key light
the energyser will do just fine, if you wanted to clip it on your hat, and run for hours on end, and have high brightness then go for the photon style.
even though the total size of the 3 alkaline cells is bigger, i would bet that in total output power the 2 scrawney lithium cells will outrun them. BUT the 2 lithium cells will run overdrive for longer. And they both will drift down in output so much that its . . .
its more a matter of personal taste and use style, and how it goes in your pocket, or goes Off in your pocket when you dont want it too.
just get both
if you think it looks cool, get it . but every 2x2016 i have vrses Ag13x3 is like night and day, with the lithium being brighter and lasting much longer. but they are 2 different designs, so i cant be positive.