is it harder to get into graduate programs than undergrad?

While the number of undergrad admits per year varies little, the quality of the competition varies considerably. If your application to Harvard College hinges primarily upon the ‘hook’ that you would be the starting goalie for the Harvard field hockey team during a year where the team has already admitted somebody else to be the starting goalie, well, you probably won’t be admitted to Harvard (at least, not with that hook). If you had applied in a different year when the team needed a goalie, you might have been admitted. See below.

Actually, there is something that such PhD applicants can do: Simply wait and apply again the following year. After all, nobody needs a PhD, and certainly nobody needs to start a PhD program under a certain timetable. If you’re not admitted to any PhD program that you like, you are well within your rights to try again another year.

Reapplying is far less prevalent in undergrad admissions (although perhaps it should be more common). Generally speaking, you only have one shot at admission as a freshman to an undergrad program with perhaps another shot as a transfer student - yet transfer admissions at the top schools are generally far more difficult than are freshman admissions (with schools such as Princeton outright prohibiting transfer admissions from 1990 until just last year). As a high school senior, if you’re not admitted into any of the top undergrad programs, too bad, it’s generally understood that you’re stuck with your safety school. {Perhaps this ought to change and more high school seniors who are not admitted to their desired college should pursue other goals for a year or two and then apply again.}