There's a catch with Remote Play on Xperia, though....
"The Japanese company even says that PS4 Remote Play will be "theoretically" possible over a web connection, but is hedging its bets by recommending that you have both the console and remote device hooked up to the same Wi-Fi network and plugged into a fast internet connection."
Meanwhile, when you do Remote Play on the Vita, the minimum requirement you need is a reliable internet connection, so you can play PS4 games on the Vita anywhere as long as you have a fast enough and stable connection.