Now that I have done more reading (thanks to the many links and posts here), I understand that it's good to be horizontal in the water, and while you are descending. Nonetheless, in two different OW classes (both PADI), I was always led to believe we should descend feet first. I'm not sure why it's (often?) taught this way - maybe there is a good reason.
I have read in numerous places that for those who have problems equalizing your ears, a feet-first ("vertical") descent makes it easier.
It was really just the descending part that bothered us and after our first attemp and going down so quickly not even having time to equalize our ears scared us both.
Feet first descents are very often taught for two reasons, and both of them are illustrated above.
Yes, it is easier to equalize with your head up. I have seen some people dispute that, but I am sure it is true from my own experience. I do my descents horizontally, and when I find myself having trouble equalizing a quick tilt of the head toward the surface usually takes care of it quickly.
The second reason is that people might find themselves in a rapid descent as described above. If you have trouble controlling your descent while you are at the same time having trouble equalizing, you could end up with a serious problem. With your feet under you, kicking gently can help control the speed of the descent.
People who are confident that they can control the speed of their descent without the need to kick and people who can equalize relatively easily are better off with a horizontal descent, for the reasons given by others.