No, there would not be a difference at all.
When you convert anything, it automatically becomes whatever you are plugging it into. For Example. If you have USB 3.0 device that is plugged into a USB 2.0 port, it will run at 2.0 speeds. Same case is here. Because you are using a VGA cable on a DVI port, it will come out with VGA quality.
Save yourself the longrun, and use the VGA port. There is really no difference as both will most likely play the resolutions you need. (I have a monitor with VGA using 1920x1080