If you just intend boiling/casseroling them like you would older laying hens then hanging isn't necessary.
But if you want to roast them then I should hang for at least a week. Traditionally they are hung with the innards in. I once had a yearling Welsumer cockerel that I had hanging in the garage. I actually forgot about him so left him hanging for 2 weeks. He tasted really nice. Not strong and gamey, but just had a definite flavour, unlike your oven ready chickens from the supermarket.
I don't believe that just resting in the fridge is as good. For a start it's more likely to go off, as a hung bird has air circulating which keeps the skin dry and stops bacteria growing. The fridge has a much more humid environment.