The tournament UI has been broken on iOS for years. It doesn't register taps properly and some UI elements are not shown where they should be.
OTOH, the website works pretty well on mobile, scrolling aside.
In general, I also had the feeling that the lichess UI is a bit more immediate, it was easier for me to get around.
But I think a big difference is not in features or UX, but the behaviour of the players. Because of its free nature, lichess has several problems that I haven't seen on chess.com. I do use chess.com significantly less, but I've always had civil interactions there.
On lichess:
* people are free to act like jerks, since they will likely get away with it. My chat's turned off, but I can't do anything about people abandoning games when they lose, trying to pretend that they've left so that I don't pay attention and lose on time, etc.
* severe lack of gentlemanly behaviour. As an example, I don't think I've ever seen someone concede a game, it's almost always a bitter fight way past the point a reasonable player may accept defeat.
* Now that I think about it, lichess brings the worst in me. I want to crush my opponents and taunt them. Yet another reason why my chat's turned off.
Blitz is a vicious game, full of trickery. :)