As Christin stated it depends on the situation.
If you caught your "significant other" having sex with someone else and (you) ended the relationship it may well be (you) who is hurting the most! One could also muster the courage to leave a toxic relationship even though they are still "in love" with them.
On the other hand if it's matter of one person feeling as though the relationship has run it's course while the other person is content with the way things are; it's most likely that person will be affected more by the breakup. From their point of view the breakup came as sort of a shock. It's the equivalent of showing up for work and being fired.
Last but not least when you breakup with someone you have no control over how they will react. In some instances there are cases of stalking, violence, and even murder. Both people are then "affected".
"Anger is the Mask that Hurt wears."