The main series (1, 2, Nocturne ,Strange Journey). You control the protagonist, he's really the only human member that will ever be in your team. The rest of your team will be filled up with demons you have either coerced to join your side, or fused with another demon. The landscapes are usually pretty devoid of life and full of demons. The atmosphere is very oppressive and the storyline is heavily influenced by various religious and philosophical ideals. They are probably the toughest of all the games. Battles are played using a press turn system, where exploiting your enemies elemental weakness earns your party an extra turn to attack. There are multiple endings based on your alignment, Law, Neutral or Chaos.
Digital Devil Saga: This is a two part story. It has nothing to do with the main series, besides sharing things like spell names, demons you fight, and underlying themes. Battles are more traditional, as you have 5 permanent party members (3 allowed in a battle). Each character has an element and a weakness, ability levels are gained by eating your enemies. (As you are part-demon in the game). I don't want to say much about the story, only that it is amazingly well written and dark.
Persona: You play the role oh high-schoolers who are going through something extraordinary. Persona are facets of someones personality given shape and form, usually representative of their hidden feelings. The main character in 3 + 4 is the only member who can switch between persona at will, (1 and 2 let all members change), Persona's are fused, leveled, bought (with tarot cards) at a place called the Velvet Room. Unlike the other games, Persona 3 and 4 are also part sim, where you go to school during the day and fight at night, though the day isn't wasted as the people you meet, and the strength of your relationship with them (Representative by the Major Arcana in tarot) decides the strength of your persona's.
Devil Survivor: Is an SRPG. You are trapped in Tokyo by the government and you only have 7 days to find a way out. It has all the staples of SMT including the multiple endings. Time matters, so you have to pick and choose your battles, and who you talk to before the timer runs out. It's grid-based, though when you attack, you are taken to a more tradition RPG battle screen.
Devil Summoner: I have no idea. It's an action RPG. That's about all I know.