Pros
Publix can be a very relaxed workplace, at least at the store I was working at. I know others can be much more strict. Overall the best part about working for Publix is the people you get to work with. You meet a lot of good people. And Publix gifts you stock as well.
Cons
In recent years Publix has been seriously decreasing the number and value of benefits their workers, especially part-time workers, get. When compared to other employers of the same industry, Publix is shadowed by the starting pay and benefits of Target or Walmart even for part-time work. I have had it heard it said that if you are chasing $0.50, Publix is not for you, and I would say I agree with that. If you are willing to work for not enough money to support yourself or your family, Publix is perfect for you. The only way to truly do well with Publix is to pursue management positions, in which you can expect to work 50 hour work weeks regularly. I would also add that management who has been grandfathered into so many benefits will absolutely question why you would care about your pay so much.