It IS true.

Size doesn't matter.
The kitchen Door-handle spindle broke. 
B&Q tracked one to Carlisle, but not Penrith. 
On a whim I went to a local firm which I tend to forget & got one no bother; had an admire of a wee torch on display for the modest sum of a Fiver. It had a rather neat form of display - not only did it work, so I could see how bright it was, but there was a reflective surface set in the package at 45˚ to the beam so it could be directed up/down WITHOUT blinding anybody while you checked brightness.

Almost exactly 2 yrs ago I exchanged the Maglight© 2-D's bulbs for CREE, or similar LEDs. You can see the difference it made.
Alice would have told you ... I have "a thing" about torches, which I can control; but, since the Maglight with 2 D- cells would make an excellent truncheon for a copper and is difficult/impossible to easily pop in a pocket, I thought "At that price, why not?"

I was sufficiently impressed by this little one and its purchase won me the door spindle as a freebie.

Being me, of course, I had to do a comparison.

Without measuring instruments, I'd say there isn't a vast difference in illuminating quality - BUT when the beam of the Maglight is spread, a central "black hole" starts to appear; which is why it was spread no further in my test photo, you can see it starting on the left hand beam, compared to the wee fellow at full spread, on the right.
Added bonus #1:-
I can carry 5 of the little uns (NOT that I would) and it still be a lighter load than the one biggie.
A tad over 4 oz compared to close to 1 lb 8 oz.
Bonus #2:-
2 different light intensities + a strobe effect. 
NOT that I can forsee a use for that - unless I'm attacked by a known epileptic. :¬(