SAN FRANCISCO — Transportation network rivals Lyft and Uber are facing trial, after two federal judges refused to resolve whether the fleets of drivers who support their wildly successful business model should be treated as employees or independent contractors.

U.S. District Judges Vince Chhabria and Edward Chen of the Northern District of California separately decided on Wednesday that juries should decide whether Lyft and Uber have been misclassifying drivers as independent contractors.