Odorless garlic has very little antibiotic properties if any at all. Raw garlic can be antimicrobial which can affect the good and bad bacteria. If the sulfuric acid/allicicn has not been properly nuetralized it has the potential to burn the cell membrane of any microbial cell. The sulfuric acid and allicin can also burn the tissue lining of the gut causing inflammation. Odorless garlic is the best option for people with gut sensitivies(as long as they don't have sensitivties to sulphur compounds).
Enteric coated garlic or raw garlic is a very bad idea for people with a sensitive gut. I found my case to get much worst with raw garlic or enteric caoted garlic as it produces a strong inflammatory response in the gut( especially for those that have a sensitive gut).