Pros
Publix is employee-owned and therefore is not as concerned in making a profit and is more apt to treat their employees well. Managers always try to do the right thing and are generally nice to you as an employee. Publix considers itself a family and therefore it is fairly easy to grow within the company, would you like to do so. In general, Publix always promotes from within. Publix does not lay off anyone for any reason and in order to get fired, you have to be doing something really bad. Publix pays over minimum wage, although not generously so, but they are flexible with your schedule. Training is great for the Deli department.
Cons
Publix has a good stock option/401k plan but unless you are a manager, other benefits are rare. The insurance is not worth it, but you do get a Christmas bonus. As mentioned as a pro, it is very hard to get fired which means that some managers who have performed extremely poorly, just get transferred to another store and not get fired as they should. Very difficult to get full time if you're a regular employee.