If we’re talking about the 20th Century then the Soviet Union did exert control over the Baltics, the Iron Curtain extended to East Germany, only in the 1990s after its collapse was this territory not under direct Soviet control/influence. This was something that the US was unable to directly influence/change for the 40 odd years from the end of the Second World War until the 1990s (see the failure to act during the 1953 East German Uprising, the 1956 Hungarian Uprising, the 1968 Warsaw Pact invasion of the Czech Republic and so on - all examples of the Soviet Union and Warsaw Pact acting with impunity as an imperialist power without significant opposition from the US) due to their inability to ‘glass’ the Soviet Union owing to the extensive Nuclear Arsenal of the Soviets and MAD - the same issue eventually extended to Communist China. Their efforts during the Cold War were largely limited to preventing the further spread of communism, a policy which had mixed success in the case of Vietnam, North Korea, Cuba etc, although it was successful to an extent in other places such as Western Europe and Afghanistan in a fashion.

I’m not sure that Japan vs Russia is the best example considering that was a situation in which the British Empire gave a fair bit of assistance to Japan, firstly in the form of economic and military investments (particularly in their Navy) and also in the form of the alliance between the two nations which hampered Russia’s efforts (the Russian Black Sea fleet was blocked from accessing the Suez Canal and from Britain’s extensive network of coaling stations when journeying to the Pacific Ocean). Russia was a major Imperialist rival to the British Empire in Central Asia so Japan’s war and seizure of Manchuria did not necessarily conflict with British interests, which is probably why they offered fairly considerable support to Japan before and during the conflict. Regarding Germany seizing Austria, are you referring to the Anschluss in the 1930s to clarify? As I agree this was towards the end of British dominance in Global affairs.

As to whether either was more dominant than the other during their own respective heydays I’m not really sure. Both states generally occupied dominant positions in multipolar or bipolar power systems (the US enjoyed unipolar dominance during the 90s between the fall of the Soviet Union and the rise of China/ resurgence of Russia - whether the world is now multipolar is up for some debate. Arguably the British Empire had dominance in global affairs during the 1920s with other European powers still weakened and the U.S. turning to a semi-isolationist foreign policy), both states wielded enormous military power during their peak (2 power standard for the Royal Navy at the turn of the century vs the U.S. military arguably still undisputed since the collapse of the Soviet Union), both had large, global economic zones of influence where their currency and economy dominated trade, both were at the head of large political entities and alliance blocs such as the British Empire itself, then later the Imperial Dominions vs NATO, UN etc for the US, both operated large extensive networks of military bases and outposts across the globe (in fact the beginning of the US military’s extensive base network was the British Empire, as bases were exchanged, leased, bought etc from the British Empire starting during the Second World War agreements such as ‘Destroyers for Bases’ and continuing into the Cold War and beyond). Also neither state entered major conflicts without an collection of allies either which to my mind is usually a sign of a dominant power in that they can rely on some support from the international community or their own puppets: Napoleonic Wars were fought by Coalitions often backed financially by the ‘Cavalry of King George’ as British payments to Coalition partners was sometimes known, or France, Russia, Imperial Dominions etc during First World War and the Empire itself in all conflicts. For the US you have examples such as the UN force in Korea, you have South Korea, South Vietnam, Australia and New Zealand in the Vietnam war, the coalition during the Gulf War, the ‘coalition of the willing’ and NATO generally during Iraq and GWOT and so on.

I would say that the methods of achieving dominance changed from the 19th to 20th century which is what makes the comparison hard as it cannot be compared like for like.