For example, in the late 20th century US GDP was double and military spending was about five times that of the second largest countries.
Those are gigantic differences! So I was wondering how they compare to British figures during the height of the empire.
Another thought, did the Cold War blunt American dominance?
By late 20th century I mean about 1970 to 1994 (don't want to break the 20 year rule).
I'd say that the United States was significantly more dominant at it's peak than Britain at it's peak. Part of this is just the nature of the times: it's far easier for the most powerful country to impact places across the world today than it was in 1850.
In 2007, U.S. GDP was more than three times that of the next closest rival (Japan). It's regularly been twice that of other countries. Angus Maddison has some data on GDP figures across time periods. GDP is generally a lot less useful the further you go back in town because of the nature of economies. I'll copy the data for Britain, France, Germany, & the United States for the years 1800, 1820, 1850, 1870, & 1900 in 1990 USD (millions).
| Country | 1820 | 1850 | 1870 | 1900 |
|---|---|---|---|---|
| Britain | 36,232 | 63,342 | 72,100 | 184,861 |
| France | 35,468 | 58,039 | 72,149 | 116,747 |
| Germany | 26,819 | 48,178 | 100,180 | 162,335 |
| United States | 12,548 | 42,583 | 98,374 | 312,499 |
And here's some data in 1930, 1950, 1970, & 1990 from AM
| Country | 1930 | 1950 | 1970 | 1990 |
|---|---|---|---|---|
| Britain | 249,551 | 347,850 | 599,016 | 944,610 |
| China | 277,567 | 244,985 | 636,937 | 2,123,852 |
| France | 188,558 | 220,492 | 592,389 | 1,026,491 |
| Germany | 258,602 | 265,354 | 843,103 | 1,264,438 |
| Japan | 118,801 | 160,966 | 1,013,602 | 2,321,153 |
| USSR | 252,333 | 510,243 | 1,351,818 | 1,987,995 |
| United States | 768,314 | 1,455,916 | 3,081,900 |
That being said, I'm skeptical that historical GDP figures are of much use, as evidenced by the fact that China & India were still the world's largest economies in 1870. Colonies aren't included and I'm not sure how best to include them. Not one-for-one.
In terms of military strength, the United States has a clear advantage. Others may be able to elaborate on the details more than me, but Britain has always been known for it's navy. Up until the Washington Naval Treaty in 1922, they had the largest navy in the world. That being said, it's army was never particularly strong (though on a man-by-man basis, it was formidable). The British Army was significantly smaller than it's French & German counterparts.
Also of note: American hegemony has been parlayed into an impressive alliance system: Of the 14 other countries with $1 trillion GDPs, the United States has mutual defense treaties with nine of them. Britain never had anything to compare to that.
Check out Geopolitical Economy by Radhika Desai, the best source for your question in my opinion.