To me at least, yes, there is a difference. I like whatsoever, even though (or because) it's a little old-fashioned. I find it the more forcefu lof the two--perhaps because it has four syllables rather than three?
I want nothing whatever to do with your half-baked plans.
I want nothing whatsoever to do with your half-baked plans.
See what I mean?
These links may help you get a sense of the difference:
I disagree, river, I personally use it quite a lot, especially when emphasis is required. Recently in another thread we were discussing the translation from Spanish about women who had had no education and there I used 'women who had had no education whatsoever' in order to stress that point. My English is decidedly BE and I don't think I'm the only dinosaur from the UK who is still using whatsoever.