DVI is a digital cable, while VGA is Analog. DVI-I has analog as well, but that is the only version of DVI with analog.
There are performance differences between the cables, but not at the resolutions we use today. Some newer resolutions are reaching VGA's bandwidth limit, which will be the reason VGA is eventually phased out. If you have a DVI and VGA port, I would recommend you use the DVI port, as it is the newer standard.