Although amend and emend overlap in meaning, there is a distinct difference to maintain. To amend is to change something in order to improve it.
- He amended the speech by making some additions and deletions.
- The members of the club voted to amend the constitution.
- I would advise you to amend your manners.
To emend is to change something in order to correct it.
- He emended the report by substituting the correct figures for the erroneous ones.
Emend seems to be losing favor and amend is taking over both meanings. However, good writers still maintain the difference.