Mostly you are talking about highly loaded single celled creatures such as Vinh's stuff...around here at least.
Direct drive lights, and with drives that, if the circuit makes them brighter with more amps...will be brighter if the cells CAN provide more amps.
For an example I use a lot - I have an XT11 that said it could take one 18650 or two CR123.
I measured the output, and, it ran longer on the 18650, but, was brighter with the two CR123's.
I then tried two RCR123/16340, and it was brighter still.
I then tried two IMR 18650 to also up the amps in addition to the voltages, and, it was even brighter than the RCR's, and so forth.
So, it is dependent upon the circuitry...but, if more amp = brighter, the higher amp cells make the light brighter.
Of course, its like flooring your car...more amps at the same or more volts, will use up the mAh in the cells faster too. The mAh on the label is NOT for its capability at 3.5 amps...its typically for one amp or less, etc.
If the light NEEDS a certain minimum amp draw to maintain its maximum brightness, the mAh for THAT amp draw capability starts to become relevant too.
IE: If a light needs 3.5 amps to be at maximum brightness, a cell that maxes at 5 amps might not be able to maintain that 3.5 amps as long as a cell than maxes at 30 amps...
So you also look at how LONG it can provide those 3.5 amps....and that's not listed typically. You look at HJK's reviews of cells for example to get that off his charts, etc.
So, none of the mass produced stuff that REQUIRES higher draw cells don't tell you...but that's a short list. As "requires" is different from "will be brighter with".
If you know the drive type, it will tell you if more amps are better...but as far as "requiring", none of them typically list that unless it is.
I just use light measuring equipment to measure the differences, and, optimize from there.