This thread is about the feature itself, not the tech behind the feature. The feature, i.e. backwards compatibility, is the same in both cases, possibly even a bit more comprehensive in the WiiU's case if I remember correctly.
It's not the same though. The Xbox One's backwards compatibility doesn't boot the console into an Xbox 360 mode, isolating you from all the other OS level features the new console enjoys. On X1 360 can be snapped alongside other apps, you can share screens/videos of the to your activity feed, you can stream them over Twitch etc. You havce access to not only 360 parties and chat, but also still X1 parties too.
They're lacking in terms of the games right now, but the feature itself is far more impressively implemented than the standard "put an Xbox inside your Xbox" solution for BC.
Actual new features: Off-tv play.
Wouldn't the PSP prevent this being an actual new feature, rather than a now widespread one?