Well you basically stated the main differences. Early june will have slightly shorter hours especially during the week, with July having longer hours. July will most likely be HOT, whereas june can be hot, or nice and comfortable, or cool and chilly.
I personally would go in june, but then I would choose cooler weather and less crowds, over crowds and hot and sweaty. But since I live here, I usually go all year round.
You have a better chance of having less down for rehab in July, and entertainment running 7 days a week, whereas in early june (before the 15th) you have grad nights a few nights a week, and some of the entertaiment (parades, shows, fireworks, fantasmic, etc. ) doesn't run every day, but will be on the weekends.
However since Pirates isn't due to open until the end of June, if you want to see what they have done, then I would wait until July.
Other currently scheduled Rehabs
06/17/2006 - 06/26/2006 Tom Sawyers Island
06/21/2006 - 06/27/2006 Sailing Ship Columbia
06/24/2006 - 06/24/2006 Mark Twain Riverboat
in DCA
05/30/2006 - 06/08/2006 Francis Lady Bug Boogie
Currently nothing scheduled for July, and they generally only schedule things for July if it is really needed, otherwise everything is open.