Are the two sentences below both correct? If so, which one sounds more natural? or are there any correct expressions else?

(1) I would prefer to walk home rather than take a taxi.
(2) I would rather walk home than take a taxi.

By the way, I also noticed sometimes the verb following "rather" is in its ing form.

eg. He took the blame rather than blaming someone else.

Is that correct? Can I use blamed or blame in this case?

Question

Are  the two sentences below both correct? If so,  which one sounds more natural? or are there any correct expressions else?

(1) I would prefer to walk home rather than take a taxi.
(2) I would rather walk home than take a taxi.

By the way, I also noticed sometimes the verb following "rather" is in its ing form.

eg. He took the blame rather than blaming someone else.

Is that correct? Can I use blamed or blame in this case?

Answer

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.

Answer

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

Answer

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