끌다 means "to cause to move in a particular direction by or as if by a pulling force"
당기다 means "to cause to move toward oneself or itself"
당기다 has a nuance of reducing the distance between two object
But, 끌다 doesn't have that nuance.
Generally, 끌다 more similar to "draw"
당기다 means "pull"
밀다 means "push"