Yes, I agree that handhelds are the new home for old school sensibility games like JRPGs, but they are also great for visual novels, which took up a lot of my gaming time in the 00s. The 3DS is your best bet since it can play DS games too, but there are titles worth checking out on Vita too, though they are few in number.
The PS4 is a good home for action games like Souls/Bloodborne, Metal Gear, lots of titles that have not come out yet (I am especially looking forward to Nier 2 and Horizon: Zero Dawn). In spite of having been out for two years, the PS4's library is still kind of in wait mode, which is one reason the WiiU seems like a way better buy right now.
To be honest, the PS3 is still a pretty good buy too. Persona 5 is on the horizon, which should be awesome barring a disaster, and there's a great back catalogue of games on the system that still feel modern despite the system's age. I can't speak for the 360; I never got one.
Another advantage of the PS4/Xbone is that if you can't afford a quality gaming PC or don't have the patience to learn how to patch games and such, a console is guaranteed to play the games you buy with no fuss, so for many it's worth having the console version of a multiplat game even if it is "better" on PC.