Their job descriptions actually aren't that similar.
The green berets are force multipliers meaning they infiltrate other countries, train the local population and use them to help their cause. They train regular civilians how to fire a weapon and the necessary tactics to be successful in combat. Being a green beret leans more towards the intellectual side rather than the physical side (but don't think that green berets are weaklings because they're definitely not) Green berets are required to speak a certain number of language and have to pass several aptitude tests.
Navy Seals are used in special missions (i.e. counter terrorist, infiltration, etc) They are the best when it comes to getting the job done with efficiency and effectiveness. These are the guys you turn to when sh!t hits the fan.