The box in the General System Preferences should work for what you want. It appears it is not being set. I played around with it and it seemed to not set the preference every time, which may be what you are seeing.
First, open up your ~/Library/Preferencese/ByHost folder and delete the com.apple.loginwindow.<long alpha-numeric string>
Then, copy and paste this command into Terminal: defaults write com.apple.loginwindow TALLogoutSavesState 0
The file you deleted is the one that stores which apps and windows are open.The command directly writes the preference for saving the logout state. You can read the setting by using this command, although it should reflect the setting in the General System Prefs, now.defaults read com.apple.loginwindowLook for the line with TALLogoutSavesState. It should be 0, now. The checkbox in the shutdown dialog will remain checked, but you won't need to change it. It should ignore that since the main preference is set to not save state.