LONDON—The chief executives of Royal Dutch Shell PLC and ExxonMobil Corp. laid out contrasting visions this week for reducing fossil-fuel emissions, illustrating a divide between American and European energy companies ahead of a United Nations climate-change summit.

Rex Tillerson, CEO of U.S.-based Exxon, said Wednesday that innovation, free markets and competition were the best tools for curbing emissions. His remarks came a day after Ben van Beurden, chief of Anglo-Dutch giant Shell, said technology wouldn’t be enough to...