They are same.
친구와 함께 영화관에 갔다.
친구와 같이 영화관에 갔다.
I went to the movie theater with my friend.
As for 'formal', it doesn't matter which one you use it.
2. August 2015
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함께 and 같이 are almost same in the meaning of "together(with)"
Both are formal.
But 같이 has another meaning 'like'
Refer to http://www.italki.com/question/92819
2. August 2015
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