He took the blame rather than letting someone else take it. This makes it clear that the subject is not doing the blaming. In your second sentence it remains ambiguous. The second sentence suggests the subject has the option to blame somebody else if he wishes to do so. My sentence suggests the subject is being blamed by another person who may have blamed someone else if the subject had not accepted the blame. Blaming can be a tricky business.

You could say 'He blamed himself rather than blaming others'.

Use blame, it's a present participative tense. Whereas blamed is past tense. Hope I helped