LITTLE ‘MANNERS’ LESSON WITH THIS: 

If you meet anyone who is older than you, never never never just ask what they’re doing using the second phrase I put at the bottom. 

If you are a young adult/teen or somewhere around the age, using the second phrase of “뭐해?” to ask anyone younger than you/the same age as you is all right. 

If you are a full-grown adult, and you first meet up with other adults who may be around your age, IT’S BEST TO NOT ADDRESS THEM AS PEERS. 
It would be more appreciated if you asked “뭐하세요?” especially if you are not very well acquainted with that person. [It’s a ‘respect’ thing].

Once you develop friends whom you can consider close, using “뭐해?” is more common.