Is alcohol or marijuana more damaging to the overall body and why?

Alcohol wins all the prizes for damage to the body over marijuana by a huge margin.

For number of people killed outright by the drug, alcohol leads with about 100,000 deaths per year, compared to no recorded deaths in history for marijuana. See How many people are killed by drugs?
http://druglibrary.org/schaffer/library/basicfax3.htm

Every major government commission report in the last 100 years has concluded that alcohol and tobacco are both more dangerous than marijuana. See Major Studies of Drugs and Drug Policy - http://druglibrary.org/schaffer/Library/studies/studies.htm

The World Health Organization studied the issues specifically and found that both alcohol and tobacco are far more dangerous to the health in every respect than marijuana. See A Comparative Appraisal of the Health and Psychological Consequences of Alcohol, Cannabis, Nicotine and Opiate Use - http://www.druglibrary.org/schaffer/hemp/general/who-index.htm

It really depends on how you use it. One glass of wine a week, a beer with dinner or a shot to get you asleep are all far better than getting completely stoned and losing your job because of it. However by the same token marijuana can calm down a person with anxiety disorders, relieve the pain of a long-term cancer or Arthritis patient and many other things and these effects are far more useful than sculling alcohol until you pass out and get liver and brain damage, or by smoking a pack a day before dying age 40 of lung cancer.

Each has its positives and its negatives, and it is people that makes each good or bad, not the drug itself - citing reports on marijuana use and comparing it to alcohol and tobacco is pointless, since so many people can and do use the latter while the former is underreoprted and very biased.