Difference - Governing Body's Approval
The ISL had the approval of its governing body, the All India Football Federation, from the start. The agreement between AIFF and their commercial partners FSDL (Football Sports Development Limited) allows the latter to create any new competition and determine which players and teams participate in it. Thus, when the ISL began in 2014 as a private tournament that was separated from the Indian domestic league system, it had already crossed the first major bureaucratic hurdle. But that may not be the case with ESL.
Just like the domestic tournaments are sanctioned by the national association (For ISL, it's AIFF), an international club tournament is sanctioned by the continental body (In ESL's case it's UEFA). But since the ESL is designed to directly undermine the attraction of UEFA's premier competition, the UEFA Champions League, the continental federation sees the ESL as a threat and has vowed to prevent it from materialising. They, along with FIFA and the national associations, may go as far as banning the clubs and players that participate in ESL from appearing in any mainstream football competition including the national leagues (Premier League, La Liga, Serie A etc) and FIFA tournaments (World Cup, Confederations Cup etc).
So in this regard, it seems ESL has emerged with a much more combative stance against the federations that run the sport, unlike ISL who had secured AIFF's blessings from the get go and within a couple of years actively sought recognition from the Asian football body AFC. ESL's confrontational approach has led to speculations that the 12 rich clubs are using it as a negotiation tactic to secure better deals for themselves when it comes to appearing in the UCL. Whether or not that's the case, we'll have to wait and see.