Near where I live there is a Walmart and Publix next door to each other. On most items, the Publix is usually more costly, but it has frequent deals that make a stop there often worthwhile.
Where I live, in Key West, there is a Publix next to a Publix!
I’ve been shopping at Publix for 30+ years and will continue to do so. If you study their web site and make a list, you can save a good bit of money. Publix brand foods are quite good, and, don’t get me started on their fried chicken!