Greek and Roman societies were two diametrically different society. It has a lot to do with geography, historical development, and ethnicity. Greek world was extremely fragmented due nature and geography. Greeks did not have problem to enslave each other and wage a war with each other all the time. They lacked unifying force, even Alexander of Macedonia did not unify all Greek-states.
Rome was built with extensive military force. In its peak it was as big as Napoleon Grande Armée 1800 years later as a permanent fighting force. Army was the center of the Roman hierarchy. It disposed the rulers, sold the imperial seat to the highest bidder, secured peace, access to public services, and social rise. It provided also stable monetary benefit for the members and after years of service, some place to live. Romans also held its power by force, but also carrot policy to its provinces. It was policy to "rewarding the friends and punishing enemies". Many people looked upon Rome for security, peace, stability, and prosperity. Not all provinces were conquered by force, some of them were deeded, and other chose Rome over barbarians like Noricum.
Both Greeks and Romans were extremely pious and religious. Faith had importance in every day life, and family was detrimental for survival. The idea that Romans spent every evening on orgies and brothels, is much of the Christian invention. While there is not denial that this happened, they were not defining moments of daily Greeko-Roman citizens.