Yuzu's will probably be to your liking if you despise grinding. It's short and easy, but the ending isn't the most cheerful thing ever. Most people that want New Game+ as soon as possible will most likely take that route. It's also fun to breeze through on New Game+ (if you give MC an Avian like Garuda and a hard-hitter, you can take down the first battle in literally one turn.)
Imo, both Amane's and Naoya's are equal in difficulty. Some say that Naoya's is harder, but I thought it would be Amane's(if I didn't demolish everything in NG+). I personally didn't like Amane's ending. At least I got a nice cape in Naoya's.
"Conquer your demon. Break your barricade. Let's Survive." -SMT: Devil Survivor
Amane's route unlocks Metatron and Loki. And Remiel too? Not 100% sure about Remiel, as I unlocked Remiel through Yuzu's. Yuzu's route unlocks Loki and Remiel. Yuzu's route is the only route that does NOT unlock the Devas.
I did Amane's route on my first play through. It's certainly not easy, but if you don't mind a challenge I would definitely recommend this route. Some people don't really like the ending you get with Amane, but you will get the most story here. There are quite a few plot points explained on her route that are only referenced or completely skipped over in the other routes.
Well kids you tired and your failed miserably. The lesson is, never try.
Here's my experience. I've done both Amane's and Naoya's to find they are almost the same in terms of battles and difficulty. One of the FAQ's here will tell you that Naoya is super hard while Amane is moderate and Yuzu is easy, but this is very wrong IMO. I followed this advice and went with Amane's and had trouble, but not too much trouble that I quit.
So here's the deal. If you want it to be easier, pick Yuzu. If you don't mind a little difficulty, choose which character you'd like to explore a bit more.
Total Health: 700/1000 Current Status:Frog, Poison|Total times I have been healed/hurt: 22/56
If you are going to pick between Yuzu and Naoya, go Yuzu because you will get Loki & Remiel there. If you go Amane, you get Loki & Metatron but you can't fuse Metatron yet because you need Remiel... So if you want an easy play through to other routes, Yuzu would be your best bet.