Hello,
First, please check your code, and make sure that you did not miss anything when you mapped your pins. It is like there are more than 2 pins used by them both.
Secondly, try using a separate power connection to supply them. Sometimes there would be problems when you are using USB of the laptop to drive gadgets of too high power. And sometimes that would also cause burning of USB interfaces.
Thirdly, if you just want to get the results done as quickly as possible, buy another board to drive each shield separately, and connect them with serial communication.
Good Luck!