In terms of crime situation, Chang Island is quite safe. The locals live off the tourist business and make sure there are no problems. Of course, you shouldn't carry large sums of money, be careful in transportation, cabs, and if staying in the private sector, make sure the doors and windows are closed. But, to be honest, these are extra precautions. There is almost no theft here, except if you are unlucky with your bungalow neighbors. But that can happen at any resort.
Credit card scams do happen in Thailand, so be careful about this. And remember that drug use and distribution is punishable by death in this country, foreigners are also very risky when dealing with drug dealers. Just be careful if something is offered to you.