Permanent Residence is automatically acquired under EU law after five continuous years of exercising treaty rights in another EEA country.
British citizenship is granted after meeting various requirements.
Permanent residence can be lost if you stay out of the UK more than two years.
British citizenship is not lost, though it can be revoked in exceptional circumstances.
You need to be a British (or Commonwealth) citizen to vote in the (parliamentary) General Elections and the upcoming EU Referendum.
Conversely, rules for British citizens to bring their non-EEA family members are much harder than those for other EEA citizens. So, if you have (or plan to have) non-EEA family members, don't get British citizenship.
No, you don't have to apply for British citizenship. It is, as CR001 said, a matter of choice. That may change if the Referendum is in favour of leaving the EU.
The Home Office does not care about your other nationalities. If you were a dual British/other national, while in the UK, you would be treated as if you were solely British. That is
international practice. So, I am fairly certain that in Sweden, you would be treated as solely Swedish, no matter how many other nationalities you hold.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.