They're both natural. The question is, do you face the problem or does the problem face you? Some have recently argued that if I'm facing you then you're facing me. Obviously, it's not true literally. But is it true figuratively, as in your two examples? I would say no.
A problem may be coming toward you in the figurative sense (i.e.the problem is facing you / you're faced with the problem), but you may be unaware of it, or deliberately ignoring it. So in the figurative sense, you're looking the other way.
- A.