It is generally cheaper to adopt.
Most shelter animals cost between $200 - $300 (Cats-adult) and $400 - $500 or $600 - $700 (dogs-adult, small and large respectively)
Animals from shelters include basic shots (not rabies or leukemia, sometimes FIV AIDS), deworming, spay or castration, microchips, collars (CATS ONLY) and usually a 30 day insurance plan, dewclaw removal (frontal onychectomy/declaw is left for buyer to determine) in their prices.
Breeders don't usually spay/castrate, microchip, or do dewclaw removal so you would need to pay for this separate from the adoption fee.
Most animals from breeders are $800 - $1000 for mixes (adoption fee alone).