Hi,
You can read some theoretical articles below:
hxxp://www.ee.bilkent.edu.tr/~microwave/programs/magnetic/dcoupler/theory.htm
replace x with t
Basically 3dB couplers are used in application where you need 2 (quasi )identical outputs (power level) with 90/180 degrees phase difference between them (typical apps: balanced amplifiers, mixers, etc). Important figure of merit for these apps is the phase balance between the outputs of the coupler.
while directional couplers are used in apps where you need the main output with low insertion loss, and the coupled output with a small percentage of the power level. (for example output power level measurement, AGC loop, distributing/summing different signals, etc)
The couplers are also known as quarter wave couplers, and if you want to increase their bandwidth, you have to use multiple sections.
rgds, Al