For the New Game+, you keep all the money of your previous games, as well as all the non plot related equipment and the undisclosed data of the normal enemies (the list of 6 attacks) . You can also fight against a secret boss.
This time I played as a female main character (that is very cute when running), and picking Rani route with Archer and Rin route with Caster. Rani and Rin routes are not really that different, since both characters fulfills the same role.
Archer is an unnamed war hero because the people already forgot about him, but is clear that is the same Emiya from Fate/stay night, even doing references to the original Kotomine and even an indirect one about the original Saber. I suppose that in Rin route he will say something about her, but since I picked Rani route, he was literally standing there with the arms crossed while Rin was dying ;_;
Caster is a cheerful and extremely loyal Servant that wants to become the faithful wife of the main character (even if is female).
She's directly related with Amaterasu, but her divinity was heavily downgraded in the Moon Cell (loosing eight out of her nine tails in the process) and according to herself, she's not really a fox but a jackal.
Out of the 3 Servants you can choose, she have the most funny dialogs due to her Magical Amber-esque quirks, but her low stamina and the heavy dependence of her skills made her the most difficult character to play with.
The main difference between Rani and Rin routes is that you fight against a different Master-Servant pair in the 4th and 6th battle.
This is because you'll end fighting all 7 classes of Servants, so if you save Rani you'll fight another Berserker and if you pick Rin you'll fight another Lancer.
In Rani route you fight against:
Gatou is a guy that mixed several religions, and worships his Servant as a God. His objective is to save the humanity via his self-made religion.
Arcueid as Berserker is somewhat weird. Is never explained how became a Servant, her status are downgraded due the ineptitude of her Master, and after the battle she comes to her senses, tears the virtual world with her claws and simply jumps out of scene. Most likely, is the true Arcueid and not data from the Moon Cell.
Lancer: Cú Chulainn
This Rin is not the same Rin from Fate/stay night, but is part of the same lineage of Magus. She's an activist that fights against the Harvey family, so her reason to participate in the Holy Grail War is to stop Leo. As I said in previous posts, her real world self is blond.
Lancer identity is Cú Chulainn. He doesn't have many lines of dialog, but is safe to assume that the data of this Lancer is based in the same Lancer from Fate/stay night, despite that Tron outfit.
In a New Game+, if you do all the Taiga's requests, a tiger vacuum flask appears in the place of Taiga, and allows you to fight the secret boss in the last arena: Ryougi Shiki.
"Yeah. I don't have any business with that woman. If you act obediently, I won't draw my hand."
She seems to be lost in the Se.Ra.Ph system, wandering around and killing Servants. Her real name is not mentioned (except in the credits titles), and the Servant class is Monster.
After the battle (by far the most difficult of the game), you get an useful item that carries to a New Game+ that nullifies an enemy attack.