Guess Ecole Poly is good enough. Is ENS more like the Harvard/Oxford, and EP more like the MIT/Cambridge of France? This would be my layman reading of the situation, charitably not invoking politics.
EP and ENS are both excellent schools. I am a mathematician and mathematics is more traditionally associated with ENS than with EP, but I've met excellent mathematicians, at all level of career (from PhD student to full professor) from both schools.
My impression is that all the French Grandes Ecoles are trying to expand their range of activities and subjects, reducing the level of diversification.
Well I guess "more traditionally associated" is one way to put it, but... 11 out of France's 12 fields medal came from people who studied at ENS. The only other country to even have 11 or more fields medal is the USA at 13. They literally exude math competency.
Having been in the selection in grande ecoles - and having been in one of those myself - EP is definitely a school of engineers and ens a school of researchers/professors. All of our teachers were from ens. Not that there aren't researchers in so or my own grande ecole but I have seen people refuse to go to ep to attempt and the next year. But those schools really are top notch, each in their own way.