They’re interchangeable S/N for conditional (‘would (be)’) - but byddwn also has a non-conditional meaning (habitual imperfect) which is countrywide. In other words, even the gogs use byddwn when they mean hab impf.
Conditional:
N - (Ba)swn i’n mynd yno tasai gen i ddigon o bres
S - Byddwn i’n mynd yno pe bai digon o arian 'da fi
I would (conditional) go there if I had enough money
Hab impf:
N and S - Byddwn i’n mynd bob bore i’r dre
I would (=used to) go into town every morning
Thank you for clarifying re habitual past (something I was explaining in an ESOL context just last week 
) but I was sure I’d come across something else… And I’ve found it! – L2 Welsh 24n, from start: e.g. Byddet ti’n dweud wrtha’ fi, fysat ti? has byddwn and baswn forms in the same sentence, both translated as ‘would’, both looking more conditional than habitual to me. Is that just elegant variation, or what? Or should I be paging @aran and @CatrinLliarJones to account for themselves?
Yes, as I recall, more conditional in the challenge. Going back to English, I think it’s possibly also a Northern thing. I like it because it feels less forceful. I’ve been picked up for it in work (Bristol area), for saying “I wouldn’t say that” instead of “No, you’re wrong” or similar.
Combination there of a very deliberate decision to mix stuff up à la stryd, triggered by a ‘staying within the boundaries of what we’ve already introduced’ situation…
Yes.
Love the way that there’s pretty much always an answer to any SSiW-type question that pops into my mind, somewhere on this forum.
Today it was the turn for Baswn/Byddwn i! 
Thanks for the above.
Here’s a good example