Unless you've given up parental rights or had a crappy lawyer, it should have been included in your divorce decree that your ex be required to inform you of changes like that. She wouldn't have to get your permission, but she should have to inform you. At the very least your kids should have told you when you had them for your time this summer, if they were aware things were changing. However, that's a whole separate matter from the difference between the schools, which I have no personal experience.
I do suggest you do some research starting with the district website, greatschools.net, and measuring up -
Measuring Up
Those will at least give you basic statistics for comparison.
Then check the police department websites for crime stats in the area to see about safety issues.
Of course it would be much simpler to just communicate with your ex to find out the reason they changed schools.