The broad breasted will grow fast and give you a good sized carcass pretty quickly, where heritage varieties will take a lot longer and the carcass will always be lean compared to the broad breasted. Broad breasted come in bronze and white, white will look cleaner when butchered, bronze will have dark spots where the feathers were plucked from.
Broad breasted can't reproduce naturally, and share the same problems as meat chickens, mainly Cornish crosses, they can have leg and heart problems, and shouldn't be kept long termed, and are best butchered.
Heritage varieties, are lighter of weigh, come in many different varieties or colors, are slower growing, can reproduce naturally, fly up on things and should generally live 4-12 years.
Those in stores are all broad breasted.