In agreement with what has been said above.
I have alloy Burkes in Low D, Eb, E, F, G, A, and high D (session bore) and they all play remarkably alike.
I’ve also had a vintage Overton Low E, which played very much like Overon Low Ds I’ve had.
So it seems to me that the playing characteristics of Low Ds and Low Es from a particular maker are going to be very similar.
This all being the case, and having owned/borrowed/tried Low Ds from twenty or so different makers, I would say that Burke’s distinguishing characteristics are
-Good scale.
-Octaves spot-on, at least to my natural way of blowing octaves, and right in the middle of Low Ds in general. There is one quirk most Burkes have, and that is that B in the low octave is a bit flat, whereas B in the second octave is not; were you to carve out the B hole to get a perfect Equal Temperament B in the low octave you end up with a slightly sharp B in the second octave. I can’t recall encountering this with any other make of whistle. It was especially noticeable both on my Burke Low D and session bore High D.
-Good volume, and an especially full low octave.
-Exceptionally strong Bottom D/bellnote.
-Exceptionally smooth voicing over the gamut.
-High A and especially High B are on the verge of being strident or “shouty”.
-Low E that’s noticeably weaker than its neighboring notes (Bottom D and F#). Many Low Whistles share this issue. I prefer whistles which have Low E as strong as the other low notes, such as the MK.
-Unusually narrow window of pressure that works with second octave notes. These notes sort of pop out right on pitch, but you don’t have a wide range of pressures that work to allow you to play much flatter and sharper like you do on an Overton. This aspect is very noticeable if you play Burkes and Overtons of the same key back-to-back.
-Pure clear tone, but still with some character. Burkes get a bad rap for being “bland” but when I’ve played several Low Ds back-to-back the Burke isn’t the most bland, but has a timbre more or less in the middle of the pack.
-Unusually large air consumption. For any pitch, my Burkes have taken a noticeably greater volume of air (not force of air) that other makes, with few exceptions. Despite their many great qualities it’s this aspect which led me to switch from Burke to MK for my go-to Low D. With higher-pitched Burkes it’s not such a big deal; my Burke high D session bore takes about as much wind as my MK Low D.
-Not the most ergonomic. The unusually fat tube and far-spaced fingerholes of Burke Low Ds make them less comfortable to hold for long periods than Low Ds with narrower tubes and hole-spacings.
-Cool space-age high-tech look. For sure when you show up in the orchestra pit and open up a roll of gleaming Burkes in various keys everyone sees that you mean business. Orchestral/legit players are always attracted to the appearance of Burkes, and really like the way they play.
About C natural, it’s fine on all my Burkes, with my usual oxx ooo or oxx oox fingerings. Yes you have to be careful to not overblow crossfingered C natural.