There are a few ways to compare the difficulty of getting into Caltech versus Harvard. One method is to compare the two schools' admissions rates. For the Class of 2023, Caltech had an admissions rate of 7.1%, while Harvard's admissions rate was 4.7%. So, considering admissions rate alone, it seems that it may be slightly harder to get into Caltech than Harvard.
Another way to compare the difficulty of getting into these two schools is to look at the academic qualifications of their admitted students. On average, admitted students to Caltech have SAT scores that are about 140 points higher than admitted students to Harvard. So, based on academic qualifications alone, it seems that it may be significantly harder to get into Caltech than Harvard.
Of course, these are just a few ways to compare the difficulty of getting into these two schools. There are many other factors to consider, such as each school's holistic admissions process. So, it's difficult to say definitively which school is harder to get into.