Composite Vs. Porcelain Veneers, What's the Difference?

The answers are done very clearly below. However-Find an experienced Cosmetic Dentist to evaluate what you really need. For instance, sometimes bonding is better, sometimes it just won’t work. A lot depends on the skills of your dentist! Keep smiling!

Imagine Two Artists
Imagine asking two portrait artists which paint is better - oil paints or acrylics? Each artist has a preferred artistic medium, and either artist might be able to paint a beautiful portrait that looks realistic and lasts. But which one is better? If you asked the oil painter to paint you a acrylic portrait, you might not get the kind of result you were expecting. And that painter might tell you that acrylic paint is dull, drippy, and can't look real. They're not lying to you, but in their limited experience of working with a different artistic medium, they believe that the same result "just cannot be achieved." They key is finding the uniquely talented artists that can work with both both oils and acrylics... and maybe even watercolors too. See where this is heading?
Comparable Options
Composite and Porcelain Veneers are nearly 100% comparable options in the modern day. Modern composite is super strong, beautiful, and highly polishable. The difference today is really which artistic medium best achieves your desired result. Either porcelain or composite veneers sometimes requires taking the dental drill to the whole visible surface of the tooth. And sometimes no use of the drill is necessary at all for either option. In my practice, the fee for composite veneers and porcelain veneers are the same. We choose together which material to use based on the amount of damage originally done to the tooth, your color goals, the existing dentistry that may be present, etc. The key is finding a cosmetic dentist who has both training AND experience with both materials. 
Beware of Overly Strong Opinions and "Oil-Only Painters"
Any dentist who would tell you that composite is dull, weak, or has bad margins is simply not experienced with working with that material. Or their personal experience has, in fact, been very bad. This is the oil painter that tells you that acrylics or watercolor paint is a horrible artistic medium.  They are right... but only for them. Some dentists are extremely talented with porcelain. It's their preferred artistic medium, and the material they gravitate most towards as "the best." Some dentists are extremely talented with composite resins, and prefer that as their artistic medium. You might consider asking your dentist about their experience with both materials, and their experience and results with them. And if you are really hoping to weigh your options between Porcelain vs. Composite, you might choose to seek out someone who truly works with both. Accomplished cosmetic dentists will be very happy to share with you before and after examples of their work with both materials.
No matter which option you ultimately choose... BOTH materials require special care and maintenance!
Jason R. Tubo, DMD, MAGD