I usually like playing youtube videos from safari. I had my iPhone 4s before and it played them fine even when screen was locked. I could pause/play from the headphones button and everything worked seemlessly. Now on the iPhone 6, it'll pause it for a second and continue playing. Also, I have to unlock the phone and click the video once again, then it'll keep playing (it won't play by just pressing play from control center which is what i always used to do).