I assume you’re talking high/soprano D whistles.
Burkes, as a rule, tend to have a slightly bigger bore (bore ID as a ratio of bore length) than many other whistles, throughout the entire range of keys that Burkes are made in.
I know these are generalities, but in general as the bore gets bigger the low octave gets more volume and solidity.
As the bore gets smaller the 2nd octave gets easier to produce, more nimble, sweeter and more pure.
It’s a balancing act. Get the bore too big and the 2nd octave takes too much force to produce and sounds harsh or strident, get the bore too narrow and the low notes become feeble.
These issues get bigger as the whistle gets bigger.
Burkes tend to the big-bore side of things, having an exceptionally full low range and bellnote, but having a 2nd octave which is less forgiving, being a bit touchy, requiring good support and control.
So the Burke “Session Bore” soprano D is built for a full round loud low octave, The 2nd octave is fine, just not having the light “action” that many players want.
The Burke “Narrow Bore” soprano D, in my opinion, plays more like traditional whistles, with a lighter more nimble and sweeter 2nd octave. The low octave is still plenty full, for me.
Aluminum will give a slightly brighter tone, brass a slightly darker tone, people say. I’ve not owned a Burke brass, but I had Chieftain Low Ds in aluminum and brass and the difference in tone and playability was striking.