Streaming just sucks on XBox One. It takes ages to even start the stream. Besides, you have to find and install Twitch first and it is an annoying app that constantly needs updates.
On PS4, it's both very fast and very convenient. They also solved the viewers banner much better on PS4, it is extremely annoying on XBox One, especially when you play a game with subtitles (like Banjo Kazooie and Banjo Tooie, for example, where you don't even have real voice acting but subtitles only). You cannot hide this viewers banner on XBox One, it is always there. No idea what they were thinking.
I'm also not sure if streaming works very well on XBox One. Viewers never stay long, there. Even if I lower the quality (now it is on medium, before it was high - no difference). On PS4 they usually stay long and there are many more. So my guess is that it also works better on PS4. Sometimes it says that it lags on One and it even disconnected a few times. Never happened on PS4. Since this is not always the case (often there were no problems on One, either), it cannot be a settings issue. And even if it was - then PS4 would still be better since you didn't have to hack yourself through it at all. In general, it is so easy on PS4. If you have a Twitch account, it's one button click (share button), clicking on Twitch, putting in your name and password and there you go. On One you first have to install the app (like I said before) and then have to do some procedure where you have to get and send to your email account a code to verify your account or stuff. Also annoying. Everything is just way better on PS4, the menu is also better organized so that you find everything faster than on the One menu. And the menu itself is faster as well on PS4 than on One. Same goes for making screenshots and videos, so fast and easy on PS4, just two clicks.
The trophy system also is way better. Sure, 360 had achievements before PS3, so that is an excuse for the much better trophy system on PS3. But on One, MS could have implemented a better system. Instead, it's still this shitty system with the points and that does not even tell you the time when you got your achievement. On PS4 it gives you not only time and date, it also gives you a screenshot which I find very cool. I'm not the most extreme trophy hunter but it is a nice system on PS4 and I enjoy checking the trophy pics after a session.