What are the benefits of external bottom brackets?
External bottom brackets allow you to have both large bearings and a large, hollow bottom bracket spindle.  A large hollow spindle can be designed to be as stiff as a small solid spindle for less weight.  Smaller bearings reduce the longevity of a bottom bracket, so the typical bottom bracket design allows a narrow range of suitable spindle sizes and bearing sizes - to get the weight savings from a larger spindle you need to sacrifice durability.  Moving the bearings to the outside effectively removes this tradeoff.

There is an additional performance factor in situations where high stiffness is required in that the distance between the cranks and the bearings is reduced, lessening the torque on the axle.

For commuting, errands, recreational riding and other "normal" purposes a cartridge bottom bracket is almost always going to be more than sufficient.  If you are particularly concerned about durability, the SKF bottom brackets are engineered for 10 years / 100,000km of riding, but for the price a $25 Shimano cartridge will usually last what feels like forever.