Hello,
Congratulations on receiving the admit. I am a first year MiM student at ESSEC Business School and I must say that you stand a fair chance at receiving admits from the likes of ESSEC, ESCP and HEC.
Going back to your question, I believe that ,although, EDHEC is a highly respected college in the French student circuit, together HEC, ESSEC and ESCP form the creme de la creme layer of colleges offering MiM in the European landscape. ESSEC enjoys a massive brand reputation in the professional networks and citing ESSEC right at the top of your CV improves your chances of leveraging the highly dynamic job environment in France, by heaps and bounds. In fact, you'd also come across job opportunities that are exclusively reserved for ESSEC students. If I were to make a choice, I would place my bets on ESSEC over EDHEC.
Having said this, I wish you the best for future endeavors.
Gargi Kumari
ESSEC Business School (2017-19)