About the Lir I know nothing, but about Burkes I have considerable experience.
The "narrow bore" Burke (which in fact has a fullisize bore) is rather stiffer in the high notes, and less nimble between the octaves, than good vintage Generations and Feadogs.
New whistles I've tried which capture that vintage sweetness and nimbleness have been the Killarney and the Sindt.
Yes indeed the combination of powerful low notes, stiffer high notes, and pure (some would say bland) tone makes the Burke the favourite of "legit" (classical/orchestral/studio) musicians.
These are the same characteristics that make many trad players dislike Burkes.
In my experience only vintage Generations and Feadogs combine exquisite sweetness in the high notes, super easy note transitions, and dark complex tone.
Killarneys and Sindts come very close, the Sindt more pure and dark but not quite as nimble and sweet.