Can I please help with a background story about this?
In the traditional Court curtesy, you do indeed bow your head. The formal Court curtesy was historically most seen at Court [obviously!] during the formal presentation of Debutantes, and how to make such a curtesy was the subject of strict rules and even required a certain amount of training - the best 'teacher' was a Madame Vacani. Courts used to be held several times a year and always in the evening.
I know all this because generations of my family were all presented at court [the tradition finally died out in 1958, otherwise I suppose I would have beeen 'presented'].
When the present Queen ascended the throne, a lot of traditions were altered as things became less formal, which also had quite a lot to do with the fact that society [and Society come to that!] was changing due to the second world war that had just finished. Afternoon presentation parties replaced the evening Courts, which had required long dresses and trains. Instead, in the 1950's, smart day dress [like Royal Ascot day wear] replaced the long gowns traditionally made by the so-called 'Court Dressmakers'. The practice of inclining the head started to change, probably because the short afternoon day wear made Presentation parties seem a little less formal, but then word suddenly got out that Prince Phillip used to smile [only!!] at the ugly debutantes who made their curtesy in order to encourage them. Once word of this got out, debutantes suddenly began to be very, very careful to incline their heads so that they would not see whether Prince Philip was smiling at them or not or in other words, whether he considered them ugly or not!! Inclination of the head therefore became theroretically optional, but for the reason I have just stated the practice did not totally die out!
This is a long-winded way of saying that it is therefore optional to incline one's head. Therefore, both Sophie and Catherine were quite right, even though they did different things.
Hope this helps,
Alex