If your tank is large enough, add some more (an even number) angels of a similar size and this will solve your problem pretty much permanently. You can always remove any extra fish once you have 2 that pair up. It sounds like yours have reached or are reaching sexual maturity and have begun to show more aggression towards each other. If you are lucky, this will pass and they'll pair up. If not, as they may both be the same sex, you'll have some aggression like this indefinately. How big is the tank? In a bigger, more heavily planted one, the less dominant fish should have places to hide to get away and would not come to much harm. However, it sounds like your fish does not have any retreats as it sounds very stressed. Letting 'nature take her course' is not a good idea. For one, keeping fish in a tank is by no means natural in itself. Letting nature take her course under such artificial circumstances is likely to lead to the unecessary death of one of the angels. A good idea would be to seperate them into 2 different tanks and then re-introduce them in a couple of days, having re-aranged this tank, and see what happens. It'll probably only be a temporary solution though. Alternatively, remove one from this tank permanently. As lone angels can become aggressive towards their non-angel tankmates, it would be best to remove the more aggressive one so the more placid one, which is less likely to bully tankmates, is left behind.
