The question considers which country gained the most power during imperialism and why. A good starting point is the definition of imperialism (see reference to Merriam-Webster below).
The question requires substantial narrowing to be worth addressing, as arguably all nations pursue a certain amount of imperialism as they grow in power. Additionally, the concept of imperialism can be applied to any situation in which a dominant culture uses mechanisms of power and influence to control people in other cultures (i.e. even within a particular nation). That being said, the question most likely refers to the rise of nations during the age of imperialism from the 19th century to the present. In this context, the contenders are Great Britain if we limit ourselves to the period of direct colonization, and the United States if we extend this to the de facto control exercised during the superpower era starting after the Second World War in 1945. The “why” for these statements, that is the proof of them, rests on measures of breadth and depth. That is, how many nations and people came under the control of these powers, and how thorough was/is this control.
These measures are easier to assess during the colonial era, as clear statistics are available as to who controlled whom, how many people were involved, and how the mechanisms of government were linked between imperial ruler and colonial ruled. In that era, Great Britain’s reach was clearly broadest. As it was said, the sun literally never set on the United Kingdom at the end of the Victorian era. In the 1600’s, England vied with France, Spain and the Netherlands as primary contenders for colonies and resources in the areas of the world which were becoming accessible through ocean travel. Germany and Italy were late entrants to this contest, owing primarily to their not unifying as nation-states until late in the 19th century. However, by 1930, England had evolved into Great Britain, and its pre-eminence in world dominion was clear. In that year, the British Empire comprised over 13 million square miles of territory and over 450 million people. Governance in these areas ran the gamut from democratic institutions in England itself, to representative structures under the ultimate control by the monarchy in others (e.g. Canada and other “dominions”) to tolerance of local control over non-strategic matters as long as they didn’t interfere with the economic and military imperatives of the British rulers (most of the colonies). By comparison, French holdings were also dispersed globally (Asia, Africa) but did not encompass anywhere near the same number of people or resources.
After World War II, the United States largely took up the mantle of global rule. As the dominant world “superpower” and the only effective counterbalance to the rising power of the post-war Soviet Union, it took it upon itself to engineer world affairs in furtherance of various interests. The application of the term imperialism is harder to measure in direct, tangible statistics in this era, as the mechanisms of control between the US and the rest of the world are not institutionalized in direct legal structures. Instead, relationships between the US and the various other nations are represented as “alliances,” or “friendships.” Arguably, de facto control of high-level domestic and international policies for these countries is exercised through a variety of international institutions (e.g the IMF, the United Nations, and others) in which the “influence” of the US is strong or even dominant. There are also numerous examples of direct US intervention in local political and economic affairs in furtherance of US strategic or business interests (Vietnam, Chile, Central America, and more recently Iraq and Afghanistan).
It should be noted that this is a highly contentious subject, and the literature arguing the degree of imperial control by the US is massive. The student should acquaint her/himself with this material and form their own opinion as to the extent, impact, and (in)appropriateness of imperialism in the modern era.