Of the two, abuse is the more serious. Most people will avoid using it because of the serious connections it has.
Abuse is to make bad use of, or to ill-treat something. It is often used in phrases such as child abuse and abuse of power.
Misuse is to use something for the wrong purpose.
- The growing popularity of cheap beer is adding to the problem of alcohol abuse.
- I misused the knife as a screwdriver and broke it.