Well, ampdude, I could be wrong or, possibly, made observations based on less than scientific procedure. I'm sorry if I've misled anybody. I was referring to primary CR123 cells - not rechargeable. The "3 volt" RCR123s would be different.
Perhaps in my case the LAs that I have and the particular cells used with them generated untypical results. Maybe I should have been more specific than: "a few minutes" and stated after approximately 15 ~ 20 minutes the output is about the same.
The MNO3 draws almost twice the current of the MNO2 so the voltage drop is more noticeable for the lamp requiring the greater voltage along with the CR123 cells being less efficient at the higher drain. With fresh cells my E2e's output matches my Wine Light's after not that much use and continues to drop. Perhaps this is not always case due to lamp and cell variations and their pairings.