Probably not on price.
Big companies have the advantages of scale and more resources. They can charge less to win market share. Mom-and-pops cannot compete with Amazon and Walmart on price, not in the long run.
What do small businesses have? Someone with the highest levels of motivation and authority making most of the decisions — the owner.
An owner does have to push through bureaucracy, nor consult multiple departments. Things just get done, quickly and effectively.
Take customer service, for instance. For a big company, this role is often handled by a junior-level employee. Someone with limited experience, possibly underpaid, just doing her job. Now compare that to the small outfit, where the owner knows that keeping customers happy is critical to repeat business. Which customer service is likely to be better?
Owners care more because they have the vested interest in doing so. And a business that cares more is a competitive advantage in any market.