VGA is capable of displaying 1080p content. In fact it has enough bandwidth to go up to QXGA85, that is 2048x1536 @ 85 Hz, and few applications can go even higher.
The VGA is converting the digital signal to analog prior to showing it on the screen, so yes, the picture would be better since the HDMI would show the original signal directly. The higher the resolution, the more bandwidth is used by the analog signal. So at very high resolutions, a digital connection such as DVI or HDMI will generally provide better image sharpness, especially on digital displays such as LCDs. However you may not notice any difference.
Note that while VGA can display 1080p videos, it can NOT display encrypted digital content such as Blu-Ray movies. This is because of HDCP (High-bandwidth Digital Content Protection), which is a mechanism used to protect copyrighted video from being accessed by unauthorized entities. Only devices that are HDCP-compliant can display such encrypted content, and only with a digital connection.
Also please note that with
AnyDVD HD you no longer need an HDCP compliant graphics card or HDCP-compliant display to watch HD DVD or Blu-Ray discs. Also 1080p Blu-Ray movie rips and remuxes don't have any HDCP protection.