The first thing you would lose would be the allicin and its antibiotic properties. Heat breaks it down rather quickly, as do digestive chemicals. Most of the health benefits from garlic come from the breakdown compounds, rather than allicin itself, anyway, as allicin breaks down in the body and it is the breakdown components that get into the bloodstream. They're the ones that really do most of the good. Even Kyolic Aged Garlic Extract, which has been soaked in alcohol and other chemicals for nearly two years still has anticoagulant effects as well as some other benefits, and it has no allicin left in it at all.
Fresh garlic is better all the way around, cooked or raw.
Cooked garlic would seem to have less immediate antibiotic value. Doctors have indicated that the smellier the garlic, the better it works, as the smelly compounds seem to do the most work. Some of the helpful compounds are probably destroyed during the cooking process and dissipate in the form of cooking odors. On the plus side, you can eat a lot more cooked garlic than you can raw garlic, at least most people can. I usually eat a clove or two raw with cooked meals, anyway.