In what ways were the eighteenth century american and british societies similar or dissimilar in terms of the rights of individual liberty, equality of opportunity and property?

 Basically, they were very dissimilar. American society was in a formative stage, searching for reason and formulating a Constitution based on radical ideas of liberty and reason, stemming from the European Enlightenment which gave rise to the French Revolution, and from the neo-Platonist humanism of the Renaissance. 

British society, while not itself untouched by the Enlightenment, remained in many respects deeply conservative and reactionary. The Establishment was concerned to protect the monarchy and the aristocracy - the 'ruling classes' - and in general the status quo from the revolutionary ideas which were sweeping Europe and America. 

These differences led directly to the Declaration of Independence and the War of American Independence (1776-1783).