I vote for Publix. We went to both the Winn Dixie and the new Publix recently. If Publix had been my first stop, I never would have had the need to go to Winn Dixie and would have saved time by not having to go to 3 stores! (We always go to Goodings for in-store prepared meals when needed)
The Winn Dixie was adequate - better prices and selection than Goodings, but was kind of "blah".
Publix, however, had much more of a selection than Winn Dixie - including a better selection of in-store prepared foods (although I still prefer Goodings for this), a larger, more varied and fresher looking produce section and an "organic/health" foods department (not as great as Whole Foods, but a lot of the basics). The meat selection was also more plentiful and was presented more appealingly. Publix was a little more upscale than the WD, which was a little too basic in appearance and selection for me. In NJ, I usually shop at Kings (much like Goodings), Whole Foods, Trader Joe's and Shoprite. Publix was a good match for me. Winn-Dixie was more like Pathmark.