Never plan on needing either but unless the conditions are completely life threatening i would think the choice would be determined by your intended destination, known storm duration and fatigue. If I could deploy a drogue and make 200 miles in the right direction I'd do it but it's not passive and fatigue would set in if the storm is of long duration. Hanging on the end of long rope pointed to the wind and swell wouldn't be my first choice but if you can't make progress in your intended direction and heaving to won't work it's your only option other than below.

We have a large engine. As long as it doesn't fail, using it would be my first choice. In Dashew's 'Surviving The Storm' there's a section on boats that survived 'The Queens Birthday Storm', the boats that survived used their engine. The ones that didn't had either a rougher time or lost the boat and lives. Of course, If that's the plan you hope the engine doesn't fail or your in deep shit. Don't under estimate the value of a good, strong and well maintained engine in storm conditions.