I suggest to NEVER face a loose horse while mounted. Travel in the same direction as a loose one. Still be looking and paying attention, but it's better to be rear ended than to have one hit you head on. I've been working at the racetrack for the last four years and have seen my fair share of loose horses and accidents. Most loose horses are "running blind" and aren't really paying attention to where they are going.
I agree with Elaine, putting your horse and youself out of harm's way gives a loose horse a better chance of being caught and secured.
I've worked for years on the racetrack ponying horses where loose horses are a fairly common occurrence. One of the most dangerous things you can do is to face a loose horse, especially if he's running wide open. If you're facing a loose horse when he comes running by, your horse may wheel, sometimes at the last moment-throwing you in front of the runaway. Your horse may also rear straight up and possibly fall over. Besides what your horse might to, there is a very strong possibility that the two horses will have a head-on collision. A head-on collision when one horse is going full speed usually results in serious injury to one or both horses, often requiring euthanasia. The riders likewise are generally injured. It is much better to face the horse away from the loose horse. Move your horse to the side of the path the loose horse seems to be taking. In an arena this would probably be toward the center. Jog your horse. This will help answer his instinctive need to run with the loose horse. If the loose horse comes right up behind you, your horse may jump forward when the loose horse is just behind or beside you, but your horse should come back to a jog fairly easily if you remain calm. The worse thing that will happen is that your horse may take off with you for a short distance. That is much better than having him wheel out from under you(possibly throwing you in the loose horse's path), falling over backwards, or colliding with the loose horse. I found most of the points in this article to be spot-on, but facing your horse toward a loose, running horse is a seriously dangerous thing to do.