I work in the supermarket business, and generally the front page "hot prices" in regular supermarket fliers are better than price clubs. That being said, you have to shop around, do your homework, and maybe wait for certain things, but you certainly can find deals at the local supermarket on bulk things like 12pk paper towels, etc.
That being said, the prices at Costco are generally more consistent, and somewhat better, in certain areas especially. For example, the whole pork loins are always 1.99/lb, where you can wait for the supermkt. for the same sale price. Costco wont go lower though either, where you can search around for a 1.77/lb. Arbirtrary perhaps...
I do not buy a ton of stuff in bulk, but will go up there once in a while for bbqs, and stuff like that. Their b-day cake prices blow supermarkets away. Literally half the price.