It's a tough call between Navarro and Dunn. Navarro and his contract were a huge albatross around the neck of the White Sox back in the 90s. To make matters worse, he had a bad attitude. But, at least the Sox were able to salvage that fiasco by trading Navarro to MIL for Valentin and Cal Eldred. Unless the Sox can miraculously pull off something similar with Dunn, I'm giving my vote to the Dunn signing.
One of the worst things about the Navarro FA signing is that Sox ownership took their own stupid decision to throw a lot of money and a long term contract to an unimpressive player like Navarro and used it as an excuse many years afterward of why they won't sigh pitchers to long term contracts.
My concern is that they'll use the same reasoning after the Dunn signing. The Sox tried and failed, therefore they'll never try again. We've already heard some of this logic since 2011: well, the Sox went "all in" and spent a lot of money on a high priced free agent and the fans still didn't show up. Conclusion - Sox fans won't support even a winner. Nevermind that the 2011 team was an utter disappointment and very low expectations drove advanced sales for 2012. In this regard, I think the Dunn signing could haunt the Sox long after his contract is over (just as happened with Navarro).
White Sox Baseball 2011-2016*
*except for 3 months in mid 2012 and 5 weeks in early 2016