The answer surprisingly is no.
Metal hardness is measured by what is called the Vickers scale where harder metals receive a higher Vickers score than less hard metals. 9ct has a Vickers hardness of 120 and 18ct has a Vickers hardness of 125. This shows 18ct as harder, but the difference is so slight that in practical terms 9ct and 18ct are much the same.
Yellow gold, white gold and rose gold are all measured using the Vickers scale, and as the same carat of yellow gold has the same gold proportional content as white gold and yellow gold, each of these metals has the same Vickers score value (that means that 9ct yellow gold, 9ct rose gold and 9ct white gold each have a Vickers score of 120 whilst 18ct yellow gold, 18ct rose gold and 18ct white gold has a Vickers score of 125).
There is another difference that should be considered when comparing 9ct and 18ct. 9ct is more difficult to bend and is a little more springy and therefore a fine 9ct ring may be less likely to bend out of shape than a fine 18ct ring. However, if the ring is of a good sturdy construction neither metal will be likely to bend out of shape.
18ct yellow gold is more yellow than 9ct yellow gold with 18ct yellow gold having a richer golden color making 18ct yellow gold a more popular choice of yellow gold than 9ct for ladies engagement rings.
9ct rose gold has a darker rose-copper color than 18ct rose gold which has a more subtle rose color.
9ct white gold and 18ct white gold have a similar white color (as normally both have a rhodium plating finish (see white gold vs. platinum information page).
In practical terms, 18ct generally holds up to everyday wear better than 9ct and tends to look better than 9ct as it ages over the years. This is one of the reasons why 18ct is normally preferred for ladies engagement rings rather than 9ct.
18ct is the superior metal for lady's and men's rings provided that the ring is not a lightweight construction (Our rings are a good construction). However, 18ct is almost twice the price of 9ct, which is usually fine for ladies engagement rings, though in a large men's ring the 18ct price can be a noticeable difference.
At Gillett's we believe that for a wedding ring that you wear every day of your life is worth the difference and we accordingly recommend that 18ct be selected whenever possible.