Both are in the wrong and should be charged accordingly
Consider these scenarios
1. Person A goes to person B and punches B in the face. Fault is in person A only
2. A argues with B and punches B in the face. Fault is in A only.
3. A argues with B. A leaves. B follows to continue arguing. A punches B in the face. Fault is in both A and B. This is called "looking for a fight"
4. A argues with B. B threatens to harm A. Person A forcefully restrains Person B. Fault is in person A but mitigated by instigation.
5. Person A argues with B. B hits A with force. A responds with more force and restrains B. Fault is in both A and B.
This is not white and black. There are grey areas. For example, a person finding his SO cheating on him and responding violently will get mitigation on his case.
In scenario 5, I feel only B is at fault. A should have the right of self defense. 3 and 4 are more murky.