Electric stoves can typically use the same type of cookware used on gas stoves. As long as the material used can conduct heat efficiently, gas and electric stoves operate similarly.
Both gas and electric stoves warm a burner that transmits heat to the cooking vessel. Electric stoves, however, transfer their heat directly; the air above the burner only heats slightly. Gas stoves require a bit of space to allow the gas to combust but create a wider heating zone. In practice, both designs are capable of transferring heat quickly, but electric stoves generally boil water a bit faster.
Gas stoves have a clear advantage when oddly shaped cookware is used. Electric stove tops require contact between the cookware and the stove, which means the bottom of cookware needs to be flat. Gas stoves don't require direct contact, so cookware with bowled bottoms heat fairly efficiently. Some pots or pans may not sit evenly on an electrical stove top but fit in the grill used on a gas stove.
Because electric stoves transfer heat more quickly, some experts recommend using cookware with copper at the bottom. By slowing the transfer of heat slightly, copper enables more even heat distribution and prevents hot spots from burning food.