I emailed Eagletac and this is the reply from Nicole:
1) The P10A circuit can ran 14500, but it's not optimized. You will get 200-ish lumen at start and drops to about 130 lumen before flat-regulation kicks-in. When the input voltage is higher than the output voltage, the P10A circuit acts as a direct drive. You should have no issue using 14500 as long as it's protected with PCB at the bottom.
OK, you guys have talked me into it -
Comparisons using 3.7V rechargeable Li-Ion 14500
vs. JETbeam JET-1 MK IBS both Max - on Li-Ion 14500
very close the JETbeam might be just a midgen brighter.
vs. NiteCore D10 (Q5) both Max -on Li-Ion 14500
again close - but this time the EagleTac is brighter.
How much brighter is the P10A on Li-Ion 14500 over NiMH - I don't have a second P10A to compare - but I compared the P10A on 14500 to the NiteCore D10 on NiMH to give an idea of the difference.
vs. NiteCore D10 (Q5) Max on NiMH
this time it's pretty obvious the P10A on Li-Ion 14500 is brighter than the NiteCore D10 on NiMH.