I have been married for one year at the end of this month and it seems that the marriage is mutually over. We have no joint assets and no children; this is my first marriage, his second. What is the difference between an annulment and a divorce? Is there an advantage to one over the other?
Most likely you want to get a divorce, and because you've been married such a short time and don't have assets or children, you probably qualify for what's called a "summary" or "simplified" divorce, which will be simpler than an annulment. Annulment is an old-fashioned concept adopted by state legislatures many years ago as a result of lobbying by certain religious groups that publicly opposed divorce, but privately recognized that certain marriages were simply not meant to be.
To get a civil annulment (as opposed to a church annulment, for which you must consult your religious adviser), you must usually meet specific requirements of your state's law, such as saying that the marriage was based on one spouse's fraudulent premarital statement. For example, in many states, if a prospective husband professed that he wanted to have children, but knew this was impossible because he had an irreversible vasectomy, this might be grounds for an annulment based on fraud.
When it comes to dividing property, determining custody or child support, or other practical matters, there is little real difference between an annulment and a divorce.
Unless one of you has an extremely strong religious objection to divorce, that is the best route to take. You don't need to prove fraud or anything else -- because every state allows no-fault divorce, you only need to say that you don't get along.