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.
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
N and S - Byddwn i’n mynd bob bore i’r dre
I would (=used to) go into town every morning