TV shows are emerging as a new front in the war over digital media between Amazon.com Inc. and Apple Inc., amid their ongoing battles over electronic books and online music.

Hours after Apple said Wednesday that it would begin renting some shows for 99 cents per episode, Amazon cut its price on a similar set of shows to 99 cents from $2.99. And unlike Apple, which rents the videos, Amazon lets its customers buy the shows.

"When...