Well Publix was THE grocery store my entire life (Kash n Karry/Sweet Bay's, Winn Dixie, Albertson's) could never really compare.
But I will say Wegman's is better.
Now Wegman's only has 101 stores compared to Publix's 1200+ so I don't know if it is fair to compare them, but most people from Florida have been impressed when they see it.
Envision if Publix and Fresh Market had a baby.......Wegman's. It's slightly more expensive than Publix but slightly cheaper than Fresh Market.