In the interests of reporting negative research results as well as positive ones…
It occurred to me an hour ago that one reason for preferring ‘while’ to ‘whilst’ (or vice versa) might just be a very simple one: to avoid doubled consonant sounds.
My hypothesis was that ‘whilst’ would be (relatively) more common before words beginning with ‘t’ or ‘st’, and ‘while’ would be (relatively) more common before words beginning with ‘l’.
So I used the Google Books Ngram Viewer to see the frequency of ‘whilst talking’ relative to ‘while talking’ – and likewise for telling, taking, turning, teaching, typing and touring, as well as standing, stopping, starting, staying, staring, stepping, stirring and stumbling.
Then on the other side, I looked at looking, laughing, learning, leaving, lying, letting, leading, leaning, listening, losing and lighting.
No difference. Before the ‘t–ing’ words, the ‘st–ing’ words and the ‘l–ing’ words, ‘whilst’ is about 2–4% as common as ‘while’.
So, that’s my contribution to linguistics for today. And now I’m going to spend the afternoon loafing around.
Loafing, wait–!
Stroppy Editor 
Comments
There is another aspect to “while” vs. “whilst.” Whilst is not used in north America. To people from the US and, I think, Canada, whilst sounds really strange and pretentious. It took me a while to stop editing it out of my English colleagues’ prose!
I’m from the US and I know an equal number of “while” and “whilst” users, both in speech and in their writings. I don’t think it sounds strange or pretentious, but then again, perhaps I’m the strange and pretentious one.