No problems provided you have an onward boarding pass - printed card/home print/on your phone. Can be tedious if you have to go to the transfer desks though, especially if there is a Chinese tour group in front of you.
As already mentioned, if flight is late, CX/KA staff escort you from the arrival gate, through the staff lane at security lane, and to the next gate. These young ladies are certainly fit as they move at a fast pace and expect you to follow!
Never had a problem even when late-arriving flight resulted in 20 minute connecting time. Also very impressed that they almost always manage to get your bags across onto the connecting flight even on such a short connection.