I'm not sure what exactly you are asking for, and you should be aware that there surely are internal differences in how different Scandinavian languages treat this issue, even within the continental/insular groups. However, I can give the following description regarding Swedish.
It's true that the passive form can be formed either from adding a -s to a verb form (and remove the -r if the original form is present) or by using the past participle in conjunction with ha/bli/vara. However, a lot of forms that differ in terms of tense and focus can be formed from these are not all of them are equally used. I'll list a few below to illustrate the problem.
1. Han sköts i benet. - He shot+PAS in leg-DEF.
2. Han blev skjuten i benet. - He became shot-PART in leg-DEF.
The above two do both answer the question "What happened to the the man?" and are semantically equal. However, the latter is more likely to be used if the context is more formal.
3. Han var skjuten i benet. - He was shot-PART in leg-the.
The third does only express a temporal state of being, that is, the state of being shot, and as such is not an adequate answer to what happened to the man.
4. Han har skjutits i benet. - He has shot-PAS. in leg-DEF.
5. Han har blivit skjuten i benet. - He has become shot-PART in leg-DEF.
These two answer the question "What has happened to the man?" and as such are similar to the first two. Here, there is a stronger inclination to go with the latter in all contexts.
Without having any data to back this up, I would say that the simple passive is more common in present, both forms are equally common in past, and that the compound forms dominates in supine.
If I missed the essence of your question, please keep asking.