I use 2-1 sugar syrup. This means I use, say 1 cup of sugar and 0.5 cups of water. This yields a little over 1 cup of syrup, which basically means that I can measure the syrup more or less like sugar, i.e. 1 tsp of syrup is about 1 tsp of sugar.
There are about 4.2 g of sugar in 1 tsp, so 1 tsp of syrup has roughly 4.2 grams of sugar.
1 tsp is about 0.5 cl. So 1 cl of sugar syrup has roughly 8.4 g of sugar.
With Cointreau it's a bit more complicated. According to the website, it has 24 g of sugar per 10 cl (7.4 g per oz). This is about 2.4 g per cl.
So, per cl, sugar syrup has about 8.4 g of sugar while Cointreau has roughly 2.4 g. 8.4/2.4 = 3.5, which means that you need 3.5 times the amount of Cointreau to roughly equal the sweetness of the same amount of sugar.
So when I make cocktails with the Embury ratio of 8/2/1 (4cl liquor, 1cl citrus, 1tsp sugar syrup), then I can convert this to a Cointreau style drink by multiplying the sugar by 3.5, by using an 16/4/7 ratio. Or, to make it a bit simpler, 16/4/8 or 4/1/2 (4cl liquor, 1cl citrus, 2cl Cointreau).
Note, however, that this much Cointreau will often dilute the citrus juice. So it makes sense to add more citrus at this point. Often people will double it, giving you a 4/2/2 drink, or 2/1/1, which is a classic sidecar or margarita recipe. This isn't a bad ratio, but I find that all this extra liquid dilutes the base liquor too much, causing me to up it slightly. Bottom line, I usually opt for a 3/1/1 ratio for Cointreau based drinks.