I know that the order of rank goes emperor-king-grand duke-archduke-prince and that a Grand Duke would not have to bow to a King as they are both Heads of State, but does a hereditary Grand Duke have to bow to a Crown Prince (or any the heir of a king) or are they considered to be equal because they are both heirs?
Actually, Archduke is generally before a non-reigning Grand Duke. Ranking based on title alone is no longer practiced and was associated more with the style a person carried (the various forms of Highness and Majesty are styles not titles) than their title.
Heads of state are considered equal irregardless of their title or style. They are ranked only by years in their respective position, but are otherwise considered equal no matter be they Prince of Monaco, King of Spain, Grand Duke of Luxembourg or Emperor of Japan.
Eg. If all the monarchs of the world were attending an event together the King of Thailand would be seated first since he is the longest reigning monarch in the world (June 9, 1946) and the King of Bhutan as the newest monarch in the world (December 14, 2006) would be seated last. All the other monarchs would be seated between them (maybe not literally between them as you know tables, rows, seating and what not differ but you grasp my meaning). Just a note, I list the King of Bhutan as "lowest" because I do not count Nicolas Sarkosy in my rankings based on his position as Co-Prince of Andorra.
A major event would feature their arrivals based on rank as this. Persons of the local monarchy (and family) would, of course, arrive first others will arrive based on longest reigning monarch and within those families based on their individual rankings.
Heirs are equal and do not pay reverence (bowing or curtsying) to each other. Guillaume (and future wife) do not bow/curtsy to The Crown Prince of Japan (heir to an Emperor) or to The Prince of Asturias (heir to a King) and so forth. Naturally, you may see Guillaume take the hand of Crown Princess Victoria or another lady (even a commoner) and bow to her but his is gentlemanly curtsy based on their gender not their position or rank. I've saw Guillaume and his brothers do this for numerous ladies who rank below them or who are commoners because they are properly raised gentlemen
The King of Spain also does this for ladies (he is also a gentleman). Some royal men are, IMHO, lacking in the area of basic etiquette and do not bow to ladies in general. I prefer the style of our Luxembourg family and The King of Spain who treat every lady as if she were, well, a lady. So, don't necessarily assume that when you see Guillaume or King Juan Carlos bow to a women that they are doing it because they think she outranks them they do it because they are gentlemen of class.
If you look through the pictures on the websites of Tom Wagner or Manuel Dias covering the silver wedding celebrations of Henri and MT you will see photographs of Guillaume, Louis and Felix making beautiful bows to ladies of every rank queen, princess, archduchess, countess and even lowly commoners.
