I miss being able to send voice mails. Several of my friends still have 360's and they try and to communicate with me. Even the friends i have(on One) find it a pain to just send text messages where a 5 seconds voice mail will do.
Wireless microphone. I hate using the Kinex for certain games(microphone), as it picks up the whole room/kitchen/front door/den. Or even worse having the group chat go through the TV, and someone having a bad game then the curse words fly for everyone in the house to hear.
I miss my controller keyboard from 360. Was a great tool for typing messages, which is all you can do on the one.
I miss being able to easily find players I had just played with, with the possibility to add them as friends.
There are a lot of items from the 360 user interface that would only enhance the UI for the Xbox one. Unless I am missing something.