Hi,
For a composite video signal there is no difference. The confusion with xboxes comes because you have NTSC and NTSC-J. The only difference is the region code. Nothing to do with video. Its the xbox that decides not to out put a video signal. Its not that the TV cannot display it. You can put a PAL signal into an NTSC TV and you will see a black and white rolling image (normally). Same for the other way around.
I actually believe that its a bug in (for instance) XBMP that screws the video settings with an incorrect setting and the xbox decides to supress video. You can set an NTSC-J machine (like mine) to NTSC with the video select utility and it works fine, but the region is not set correctly.
Again I think this proves that XBMP screws up the settings.
I also have played the xbox's video back on an in-car monitor and it works fine. If you CORRECTLY set the mode to NTSC or NTSC-J it would still work. XBMP won't do this though. Even config magic does not understand NTSC-J and instead displays the mode as UNKNOWN. I suppose that because the devs did not have access to an NTSC-J machine or eeprom file.
To answer your question, you should not need to change the mode, and if you use XBMP to do so you will most likely kill all video output. If your xbox correctly outputs video on a TV but not on your car monitor then the problem lies elsewhere.