British Empire, undoubtedly. A brief comparison of the legacy of both Roman and British Empires would substantiate my answer.
Legacy of Roman Empire:
- The Idea of a Republic form of Govt.: Before Julius Caesar conquered Rome in the year 44 B.C, Rome was a republic. The republican govt. of Rome was headed by two Consuls, elected by common people and advised by a Senate. This was a revolutionary idea in an era of absolutism where a King had unfettered powers. Though democracy is said to have had its beginnings in Classical Greek city of Athens, this form of sharing of power was first implemented on a grand scale only in the Roman Empire. Many of the modern day nation-states follow similar govt structure characterised by separation of powers between the Executive, Legislative and Judiciary.
- Roman Catholic Christianity: Romans purged Christianity when it was in its nascent stage circa 4 B.C to 312 A.D. But when emperor Constantine converted to Christianity in 312 A.D. it was Rome that helped Christianity spread to far off lands in Europe. If Christianity is the most followed religion today, a lot of it is owed to the Romans, emperor Constantine in particular.
- Roman Architecture: Romans drew heavily from the Classical Greek architecture. Amalgamation between the two styles gave rise to the magnificent Greco-Roman architecture whose enduring legacy is felt even today. The White House building is a great example of the Roman architecture.
- Legacy of the British Empire:
Magna Carta and the Glorious Revolution: Magna Carta was a historic declaration by King John in 1215 AD. It was a document imposed on the King by a diverse of group of people primarily consisting of barons and merchants to restrict King’s powers. Its path breaking provisions granted much need civil liberties to people and ensured that the King’s actions were not arbitrary. This gradual move towards inclusive nature of political setup ultimately culminated into the Glorious Revolution of 1688 when Britain abolished absolutism to establish a constitutional monarchy wherein the Parliament, consisting of elected people, had the real power.
Thus as common people had more say in governance, they had the liberty to innovate without fear which is a crucial factor in making Britain the birth place of Industrial Revolution. Addendum,this broad inclusive nature of polity helped Britain emerge as a colonial power as the private merchants who are benefitting from Industrial Revolution were free to pursue trade with the colonies unrestrained by the diktats of the Crown.
Industrial Revolution: I consider this as the greatest contribution of Britain to the modern day industrial society. By the late 17th Century, conditions were ripe in Britain for the emergence of Industrial Revolution. People had the liberty to innovate and earn patents for their innovations without fearing usurpation by the Monarch as was the case with other empires of those times.
As new technologies emerged, they improved the industrial productivity of Britain drastically, marking the beginning of the prosperity that we see today. These technologies were adopted by Western Europe, USA, Canada and Australasia over the course of their history. Thus the roots of modern day prosperity lie in the Industrial Revolution pioneered by the British.
Colonialism: On the negative side, this is the worst legacy any empire has had over a vast range of countries. Africa is reeling under poverty today because of the plunder and expropriation of resources by the Europeans and British in particular when they colonised the continent. In South Asia too colonialism has had a devastating impact on the Indian Subcontinent making many nations impoverished and famished.
Fathering Prosperous Nations: In colonies where there was no significant indigenous population, the British empire had the opposite effect of Colonialism. In these colonies, the settlers from Britain rebelled against the Crown and established independent nations.These independent nations thoroughly adopted the technologies that emerged from Industrial Revolution and built strong, stable and prosperous nation states. USA, Australia, Canada are the quintessential examples.
From the above comparison, it can be said that British Empire influenced much wider geography over a far longer period of time compared to the Roman Empire. Even in terms of the significance of the impact each empire has had, the superior nature of British empire’s legacy in the modern day world is unquestionable.