One should not override the other, you should even be able to have both working at the same time and have two monitors, one from the VGA/DVI and one from the HDMI but you need to make sure your PC knows the type of signal to put out of the HDMI port (it may just simply need enabling that's all). 720p is the safest option to start with but you can check in tour monitor/tv manual to see what resolutions it supports.
I have a DVI/HDMI output and in the PC display settings it picks up the TV automatically (as in it knows there is a display connected) but I needed to set the properties properly for the picture to display correctly.