As noted, both are correct. Employing "än" as a conjunction and therefore using subject pronouns ("jag", "han", "ni") is considered the more formal option, and suitable for use in writing. When it is a conjunction, you are implying another full clause that has been cut off. The above would be Hon sjunger sämre än jag sjunger. But I'd say it is very unusual to hear in spoken language. There "än" is pretty much always a preposition, and thus you use object pronuns ("mig", "honom", "er").
On a thread about these words Arnauti posted this link:
And on this thread devalanteriel said "Not much, really. We tend to use sämre for describing qualities, and värre for situations, but either one is usually fine."
- "Alltså", not "altså"
- "Försämrats", not "försämrat" ("Försämrats" is the passive form)
- "Bara betyder", not "betyder bara"
- "Right" doesn't really have a simple one-to-one translation in that "seeking confirmation" context. I would translate it as "Stämmer det?", which roughly translates to "Is that correct?".