Actually, the power each of them held at their height was very similar, but I think the British had more power than any other country has held or ever will hold at their height.
First off, Britain held total military superiority over the world, similar to the way the United States held military superiority. The core British Army was a significant-sized force that was professional, and well-trained and equipped. And there were numerous colonial regiments from all over the world to call on, so the British had one of the largest and best-quality armies in the world (the French Army was larger, though). However, the trump card was Royal Navy, which was by far the most dominant power on the world oceans. And with total mastery of the seas, Britain held total military superiority, since no one could trade with the outside world if they were at war with Britain, and the British could freely invade any country in the world without fear of being invaded.
Note that this is written by an Anglophile. All figures taken from The Rise and Fall of the Great Powers - those with different figures are requested to provide their sources for comparison.
Army size is rather low. Let's take 1880 as an example year (used for all other figures when possible)
Military
and naval personal: Britain is fourth place (Russia, France, Germany,
Britain, Austria-Hungary, Italy, Japan, United States):
Military Personnel alone is even more dismal, although the figures are apparently not comparable, so we'll stick with those in chapter 5.
Warship tonnage: #1 by a substantial margin, yes (France, #2, has less than half of Britain's total, Russia less than a third, and the US something over a quarter).
Quality-wise, I have yet to hear of anyone describing the British army in this period as a particularly elite force, but even if it was, that's a small army. A small army mostly scattered all over this huge, sprawling empire.
Hardly an overwhelming force that can be concentrated on anything without massive wartime effort (and according strain).
However, beyond that, they held economic dominance. They produced about half the world's finished products, and their merchant fleet had by far most of the world's merchant ships (I think it was up to 90%). This in addition to them controlling a quarter of the world with all those natural resources and local industries. To maintain their economy, they needed to import millions of tons of products. So virtually all economic activity in the world involved Britain in some way, and the British could take charge of exporting and importing goods from all over the world.
"Manufacturing" is 22.9% (1st place) in 1880, but down to second place (18.5%) in 1900 and third (13.6%) in 1913.
Merchant fleet size is not given, but I would be doubtful of it being quite so high as that.
Most of those natural resources were undeveloped, and the local industries fairly insignificant.
"Virtually all' economic activity? Oh please. The world did not depend on imports or exports from Britain.
For example, a British agent would buy cotton from the US, send it home on a British merchant ship, where it would be produced into clothes and British merchants would then sell it to other countries. This was how world trade worked, with Britain almost always involved some way.
This is how British trade worked. That is not how world trade worked.
Then, there is the fact that the London Stock Exchange was the only global one. Every country did it's business through London. Every great power owed Britain something.
"Owed Britain something"?
No other country, not even the USA of today, has such an effect on the world economy. Of course, economic events in the United States affect the world, but when the US imposes sanctions on a country, it can't bankrupt them the way Britain could by refusing to trade with them or give them loans from the London Stock Exchange. For that reason, I believe the British Empire
Britain refusing to trade or refusing to give someone loans from the LSE is not a recipe for bankrupcy for the country in question, or we would be looking at a Germany bankruptcy in 1915 in WWI.
Britain certainly had many advantages, but describing its rise as inevitable or its power OTL as absolute are too much.
