Persona is heavier on story, has dating sim elements and operates off a calendar system to progress the story Hard to explain the calendar system but essentially events are timeboxed and there can be dead time if you finish the main mission quickly. Persona games try to emulate an anime.
SMT is the original series. Easier to explain: it's like pokemon with mythological creatures and a light philosophy story. I don't know if I'd recommend starting with SMT 1 or 2, even if they are arguably some of the best in the series