I've had a long-running debate on the potential issues with the series drogue on other forums. With a para/sea-anchor setup, you're bow-to waves, presenting the strongest, most "protected" part of the boat to the nastiness.
With a series drogue, you're exposing your cockpit to pooping and your rudder to potential damage from the force of water flowing past it "in reverse".
Lin and Larry Pardey have heard of rudder damage in the case of the latter. They swear by the former.
What say you?
I think the answer is going to depend greatly on the particular boat you are sailing. Boats with deep poorly draining cockpits, with large companionways could be a real problem with series drougues. Unfortunately, this would include a huge number of boats that have been sold over the past 20 years. On the other hand, I think some designs may ride out a storm better while running before the wind with a drogue out, than heaving to with a sea anchor deployed. I haven't been in conditions that warranted either, so I am just speculating based on what I have read and understand.