Was this a mistype?:
in the US students do fewer subjects that they pick themselves. In comparison, Irish students can only choose very few of their subjects,
Isn't this the same thing? Perhaps you can clarify.
In any case, in the US educational opportunities really seem to vary from district to district. I was able to take advanced science courses like organic chemistry at my public high school, courses not available at all public schools.
Greater than half of high school courses were more or less predetermined for me, though I could choose what level of difficulty within those courses (I chose to take AP Calculus while others (in the vocational track) filled the same requirement with prealgebra.
Truely "elective" courses were relatively few.