When installing kernel modules, I have the option to strip out debugging symbols using
INSTALL_MOD_STRIP=1. This saves significant disk space.
Does it also save memory? Why should one keep the debugging symbols in the kernel modules?
Debugging symbols just add extra information to an executable that helps when running a debugger such as GDB. It lets the debugger recreate the source code from the executable to show you where things such as segfaults occur during runtime.
If you are testing / hacking / making something inter-operate with the module then you need them. During normal operation they just take up space and can pose a security risk on a production machine. For example if someone breaks into your system with user privileges they can use a debugger to look for weaknesses in the current running modules to gain root access.
It will save a small amount of space to remove them as well.