As far as rechargeable vs primary runtime comparisons, this is a comparison that is not really fair to make, but I will try to summarize some of the important points:
A pair of CR123s packs slightly more stored energy than a single 18650 cell when the 2 configurations are compared at a LOW drain rate (like an LED module).
A single 18650 packs slightly more stored energy than a pair of CR123s when the 2 configurations are compared at a higher drain rate (like an incandescent module).
A Single 18650, with its lower voltage than a pair of CR123s, will operate most buck regulated LED modules at a lower (read "direct drive or less") output than would be the case on a pair of CR123s. This results in less output, but much more runtime because less energy gets used over time.
So... the answer to most of your questions will always depend on the specific configurations being compared.
If your main goal is to get really good runtime, then I suggest you take the following things under consideration:
1. RCR123s are the worst option for maximizing your stored energy.
2. Something with multiple modes will allow you to run for extended periods of time with less power consumption.