One size fits all
The problem with the first approach is that it is almost impossible to predict the disaster scenario that will result in your plans being invoked. Experience has shown that more often than not, the disaster that was planned for isn’t the one that has to be recovered from. Producing numerous plans in an attempt to cater for every possibility can result in an administrative nightmare.
Unless there are specific threats to your particular business which warrant their own specific plans (eg train/plane crash, product recall or specific technology failure) then it probably makes sense to take the generic approach and make your plans flexible enough to cater for any situation.
Napoleon said, "no plan ever survives contact with the enemy". Being too prescriptive in your planning can be prohibitive to the recovery. What will get you through is having a plan that is flexible enough to cater for any given situation and a team with the ability, authority and training to deal with whatever the incident throws at them.