I had the Direzza Star Specs on my 335 until about a month ago when I switched to the PSS.
In short, I much prefer the MIchelins.
The two tires have very similar handling characteristics as far as street driving is concerned. I have not had any experience with either tire on the track. In both cases, turn in is crisp (perhaps still not quite as crisp as with RFTs) and both wet and dry traction is superb. With the colder weather here in NC, both experience decreased levels of traction but you shouldn't have to worry about that in FL.
My big beef with the Dunlops was the INSANE road noise after about 5k miles of wear. Can't speak for the Michelins yet (only have about 500 miles on them), but I haven't read anything about noise issues. Another big selling point for me with the Michelins was the tread wear rating. I'm expecting them to last longer than the Dunlops, which lasted about 14k miles for me.
Then - 2001 E53 X5 4.4, 2005 E85 Z4 Dinan 3.0, 2007 E92 335, 2013 E82 135
Now - 2016 F15, 2017 F80