Both limit your liability, and both offer more credibility. It can be tough choosing between the two. Here are some useful comparison to help you out.
It's worth noting that there is actually more than one type of corporation. An S corp is similar to a C corp, but can be taxed in the same way as an LLC. An LLC is usually taxed as a pass through entity, meaning the profits are taxed as your personal income. A C corporation is taxed as a separate legal entity. and due to some new tax law changes, may be taxed at a lower rate than your personal income. The drawback, however, is that any income you make from dividends paid by the corporation is taxed as personal income, despite having been taxed as profits.
An LLC is extremely flexible in regards to ownership. It can issue stock to its members in any way it chooses. A C corp may issue a unique stock class to imitate this practice, but an S corp must issue only a single class of stocks, and distribute its dividends accordingly. Also, in an LLC, any member may take on any role as needed. A corporation is structures a little differently. It must have a board of directors who handle the management of the company, and officers who take on the day to day tasks.
There are benefits to each type of company, and choosing the right one is can come down to any number of factors, such as the size of your business, or the amount of money you expect to make. If you're still having trouble choosing, an experienced tax accountant can help you understand all the factors that should enter the decision.