I need a bit more information here: what is the make and model of the computer? What are you currently using now as a connection? VGA (analog) vs HDMI (digital) at 1080p is a questionable subject. Personally for me I could go either way. It really depends on the monitor, I had a monitor that had better color on VGA.
The biggest differences with HDMI vs VGA would be the ability to carry audio, and HDMI supports HDCP, which is required for blu ray playback. Outside of that, it really goes both ways. You will likely find people prefering one or the other. Personally with the advantage of audio in the same cable and HDCP support I have upgraded to HDMI.
When you get to the 4K resolution ranges your options for cables begin to go down, HDMI 1.4a and display port 1.2 etc.