In the hope of appealing to more-sophisticated consumers, fast-food chains are moving beyond simple cheeseburgers and tacos, adding fancier ingredients such as portabella mushrooms, citrus-herb marinated chicken and pepper bacon.

The move is driven by a growing foodie culture as well as the success of chains like Chipotle Mexican Grill Inc. and Panera Bread Co., a category known as "fast casual," where customers still order at a counter but are paying for something up a notch from a burger, fries and a shake.

Both...