Anything it doesn't have that you want you will have to add. Overnight trips do not need as large a boat as week-long outings. If that's you, you need a bigger boat. A bigger boat will also be easier to paddle in bigger seas than a smaller boat. Single kayaks provide greater maneuverablity than doubles.
Doubles can be faster than singles.
Doubles may be able to carry more gear, but keep in mind that they need to carry more than twice as much gear for this to be true. A double will require the use of a rudder to steer. Some doubles are more stable than a single but will be more difficult to rescue and pump dry. There are lots of different hatch designs out there. Considerations when looking at hatches are watertightness, resistance to breakage, and size.