I have a sea anchor which I hope remains right where it is underneath a lot of stuff in a locker. I guess the best option is to have both. There was a study, I believe by the USN (could be wrong) that weighed in on the side of drogues but to me putting the stern of a boat to the sea is WAY counter intuitive. A good book is The Pardy's Storm Tactics has lots of good information on using a sea anchor.
It took me a LONG time to become a believer in the JSD for that very reason (stern-to waves seems wrong). I'd read the Pardy book as well and saw the "common sense" in the bow-to approach.
However, after lots of research, and especially after reading Hal Roth's "Handling Storms at Sea", a more recent heavy weather book than the Pardy's, with its very meticulous comparison of the various tactics...I became a believer.
I also agree with Jack above on the issue of how your boat is set up to handle a boarding wave. Ours is pretty well set up to deal with such an occurrence (relatively small and shallow cockpit, top-down companionway entry - not vertical with large hatchboards, pretty good drains, etc.) - to a degree of course.
Anyway, all this is certainly hypothetical for me. And I hope it stays that way. But I definitely trust Hal Roth's take. So the JSD for me.