We do a little of both. I wrote about our extra chore list, and you can read about it here. The premise is they can chose an extra chore every day except Sunday to do for cash. They are responsible for other duties around the house which they do not get paid for such as cleaning their rooms, picking up after themselves, etc. Our goal is we want them to learn about money while they are still under our roof.
Weekly chores are something we instituted maybe about a year ago. I got the idea mainly from one of my friends when I went to her house. She had a kitchen person, a pet person, and a runner. The kitchen person helped out in the kitchen for the week. The pet person took care of pet for the week. The runner was the person the parent would ask to do various chores which needed to be done around the house such as shovel the driveway or go grab the bag of chicken out of the freezer.
I decided to make my own weekly chore list, and my weekly chores for my kids are kitchen, pet, and trash. These were the jobs which seemed to be needed the most in our house. These jobs could consist of any of the following:
loading and unloading the dishwasher
washing the dishes
setting the table
wiping the counters
helping cook dinner
giving pets food and water
poop scooping the yard or cleaning out a cage once during the week
giving the dog a bath
taking the dog for a walk
playing with the pet
emptying the trash cans in the bathrooms and bedrooms
taking the trash out to the garage
putting the trash out to the curb to be picked up
taking down recycling from the kitchen
sorting recycling into bins
Each child get that specific weekly chore for one week and then they switch. So, one week Nathan will have kitchen duty, then the next week Lauren will have kitchen duty, etc. The weekly chore is not a paid chore. It just helps out so much when everyone is pitching in to do something. It makes me a little less tired and irritable as a parent. As they say, many hands make light work. I am all for that!