Dogs adopt the strategy of "eat first, ask questions later" (as pack animals that eat garbage, carrion etc). So they are quick to vomit up something that causes trouble. Also they are more likely than humans to eat stuff that will kill them.

As for their immune system, inbreeding of dogs has caused all sorts of susceptibilities, though overall humans are a better vector for disease (density, widespread distribution, gregariousness, etc). Also humans worry about disease symptoms that dogs and other animals stoically ignore and thus the disease can go unnoticed by the human. (e.g. a bit of diarrhoea dribbling uncontrollably out your backside will probably concern you but a dog will just put up with it -- though an owner will likely object!) .