I must admit I was unaware that the PS4 added in the option to directly connect rather than go through a router. Anyways, I have little interest in connection that does not offer low latency, so the online remote play option does nothing for me.Okay, substitute 3DS with New 3DS or whatever comes after that. One thing I'd have an issue with is buying a separate controller that would only use direct communication like the Wii U <-> Wii U GamePad. It greatly limits its working range. Nintendo calls their feature Off TV Play because it's exactly that. Sony however has Remote Play and that works wherever you are as long as you have an internet connection. The good thing about Sony is that they made Remote Play better with the PS4 as it supports a feature called Direct Connect and that's pretty much what Off TV Play is with very low latency. If Nintendo can't offer the same flexibility like Sony does, then there's little point to having a second screen, either bundled or separately.
edit: it looks like even with the direct connection, the PS4's remote play still suffers from latency on the wrong side of 100ms.