Neither Java nor C# are interpreted. Both of them get compiled into native machine code.

The biggest problem with both of them and games is having to code in such a way that they never garbage collect during game play. The number of hoops you have to jump through to accomplish that nearly out ways the benefits of using them in the first place. Most of the features that make those language fun to use for application or server programming have to be avoided for game programming otherwise you'll get long pauses during game play as they go off and garbage collect.