@cmsjmt, MIT is just as holistic as the Ivies (and also take in to account gender, race, and athletic ability in some sports). Caltech is closer to Oxbridge (but also take in to account gender, though not race, athletic ability, or legacy).
In any case, the system for admissions to Oxbridge isn’t very similar to that at most American elites, so definitely some would do very well in one type and not well in the other and vice versa.
Anecdotally, more students from a third country (China) seem to do better at Oxbridge admissions than in to HYPSM, though that may be because the higher education entrance system in China is closer to England’s than the USA’s.