Bar ends were developed in the mountain bike world for hill climbing. By pulling back on bar ends you dig your rear tire into the ground creating more friction. This allows your pedal stroke to propel you further forward. To summarize bar ends help you climb hills without any extra effort from your legs. 

Short bar ends: These allow you to climb hills faster as mentioned above. Additionally riders don't want to put too much pressure in one place. These give you a couple extra hand positions. Overall these are perfect for mountain bikes and folding bikes ( since they don't get in the way of the fold ).

Long Bar ends: These also allow you to climb hills faster. They provide many additional hand positions. However these hand positions can not be used while trail riding. The furthest point of the bar end is too far from the handlebar to keep control of the bicycle. Overall these are best for commuter bikes, that don't fold ( the long ends will disturb the fold ). This is another bike part where less is more, so buy less and get more.