It is ridiculously good.
At home with a direct connection it is basically laqless. Practically 1 to1 and I have used it a bunch. In fact there was one time I played for almost 4 hours using Remote Play when I was sitting in front of the TV and just didn't bother to turn it on. It runs smooth (with a rare, quick hitch) and looks really, really good.
Away from home it is also great, but you need a decent wifi/hotspot connection and the better the connection the better it runs. I tried running it on a slow 1.5/1 connection and it connected and turned on the PS4 ok, but the game was so laggy you would never be able to play it. On anything decent (say 15/2 or so) it seems to work fine (audio lags behind a bit though).
I used it a couple days ago from my Parents house about 60 miles away. Speedtest showed their connection at 23-27 down 4.3-5.7 up (normal Comcast connection) and it ran damn near as smooth as if I was sitting in my living room. I Played Assassins Creed and got in a 3 ship battle, boarded the other ships, sailed all around and then hunted and killed an Orca, went into town and got in more sword fights and chased down a shanty. During all of that it ran smooth as butter except for during the Orca fight it hitched on me a couple times (which it will occasionally) where the stream/screen freezes for about a half second once and about a full second another time. No big deal at all