The Brits do know how to do pageantry, I don't think anyone else comes close.
Some background uniform trivia...
On the red tunics of the Guards regiments, you can tell the regiment by the pattern of the buttons down the front.
The Guards' bearskins are modeled on the bearskins worn by the Chasseurs a Pied of the French Imperial Guard at Waterloo, whom they defeated in Napoleon's final assault. A t the time they had believed it to be the Grenadiers a Pied whom they had put to flight, which is why they are called "Grenadier" regiments to this day (and presumably why the bearskins don't have a brass plate at the front - the Imperial Guard Grenadiers had one but the Chasseurs didn't).
The armour of the household cavalry was also adopted after Waterloo, the British having been so impressed by the Fench Cuirassers in theirs. The British had got rid of their armour ("cuirass") in the 18th century. This had caused a bit of a row as the cuirass-equipped regiments - "Heavy Horse" - were told they were to become Dragoons, i.e. heavy cavalry without armour. The regiments were much displeased at this, since their new regimental numbers would have much less seniority i.e. the 1st, 2nd etc regiments of Heavy Horse would become, say the 11th, 12th etc regiments of dragoons, and this wouldn't do at all for men for whom the seniority of regimental numbers mattered. The circle was squared by renaming them "Dragoon Guards", this way the powers that were made the desired expenditure saving, while the regiments kept their numbers.
Napoleon himself started a similar row in 1809, when he had been much impressed by the performance of the 1st and 2nd Carabinier regiments at Wagram. These had been uniformed similarly to the Horse Grenadiers of the Imperial Guard i.e. blue tunic with (again) bearskin headgear. Napoleon decided to "upgrade" them to cuirassiers, of which he already had twelve regiments. However, the colonels of the 1st and 2nd Carabineers were d@mned if they were going to slide down the list to become the 13th and 14th Cuirassiers and so they put their feet down. A compromise was found: the Carabiniers were re-equipped with brass armour over white tunics whereas the Cuirassiers wore steel over blue. Thus Napoleon got his two additional regiments of armoured cavalry.and the Carabiniers kept their regimental names and numbers, and everyone went home happy - especially the uniform and equipment suppliers, one assumes.
Imperial Guard Grenadier a Pied
Imperial Guard Chasseur a Pied