Correct me if I'm wrong but PS4 remote play is only over LOCAL WiFi.
While these features are cool, in order to get the full suite of features I'd be spending close to $1,000. That's a massive pay wall in my opinion. Just the PS4 is enough for me.
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It's not local Wifi. As long as your Vita and PS4 are connected to the net, you can remote play from anywhere.
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It works the same way as the psp to ps3 which is over all Wi-Fi.