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.

Edit: I also prefer mainline to Persona. Should reiterate that Devil Survivor is definitely worth checking out. Not patient gamers but the new release of SMTV would also be a good starting point.

SMT1 has a great intro but it is confusing and does not hold your hand. Some mechanics are straight up broken so you can steamroll the game if you know about them (electric bullets). All of the games are like that to some extent. SMT2 is less confusing and might have the best story in the series.