Sorry Mr Vanoord but I feel that you have missed something.
Did you do a comparison test using AA rechargeable batteries rather than the ordinary ones?
Ordinary AA battery is rated at 1.5 volts while rechargeable ones are rated at 1.2 volts. I would reasonably expect the Fenix to be an outright winner here and would compensate for the lower voltage input. I have tested the Tesco with rechargeable batteries and noticed a distinctive lower light output.
My solution to this will probably be to fit my Tescos with a better driver board if possible, and maybe even an up rated emitter. As there is a lot of aluminium in these they could be a prime contender for upgrading due to the fact that more aluminium will provide more heat dissipation.
You know what people like me are like, we just love to mess!
My avatar is a poor likeness.