Reports have said ESPN will use the same feed as NBC, and in them, NBC issued a statement that it decided not to renew because it didn't want to compete with whatever OTT service F1 presumably has planned.
While the world and media landscape has certainly changed, ESPN is not the same network that once ran RPM2Night, 2Day, and treated motorsport as a first-class citizen and with respect. Long after the races ended, it was that program that allowed it to continue coverage of the deaths of Greg Moore and Dale Earnhardt, and other newsworthy events from the racing world.
Based on how ESPN currently operates, and how it treats IndyCar, the best that could be expected is that F1 coverage remains on par with what NBC provided. In all likelihood, it will be worse.
The silver lining, at least for IndyCar fans, is for the series to be finally rid of ABC, Cheever and Goodyear, and for NBC to carry the complete package, including the Indy 500.