Which setup is going to be more efficient with longer run times?

Both optics and LED.
As long as optics is designed for throw, more or less(1) beam intensity = optics_area lm / led_die_area / C

C is a constant that depends on the LED. Most flat LEDs(*2) have it very close to each other, most domed ones have it somewhat quite close to each other and domed ones have it very roughly double of flat ones. That means: with the same die area a flat LED will have about double beam intensity

So…tripling die size requires you to triple optics are to maintain throw.

A floodier optics will reduce intensity from what the calculation shows. You can do nothing to increase throw over what the calculation shows.

(*1) This ignores optics transmission losses as well as other imperfections
(*2) Flip chip LEDs are floodier than non-flip chip ones, regardless if they have a dome or not

Would you mind referring me to some suitable examples for my OP?

http://www.international.mtnelectronics.com/index.php?route=product/product&path=67_115&product_id=357

Please treat them as examples rather than suggested solutions. I don’t know which buck driver would be the best for you.

Somewhat related to this thread… what driver/emitter combo is the best for longest run time at very low output, say 1-50 lumen range?

Just want something to last as long as possible on an AA/14500 light while backpacking.