Was the Roman Republic more successful in its army or government?
It was government in which they particularly excelled. Their system was to either use the existing local government or install a better type, but leave the locals to rule with military support from a Roman provincial governor; alternatively via a client king beholden to Rome, also with support from the Roman military nearby. Whatever the system, it meant that the country was ruled by its natural system of rule, and the local rulership took the responsibility and odium for controlling the populace and for taxes.