HDMI vs VGA - cost vs quality

Hi everyone,

So, I'd like to use my TV as a second display for my Macbook Pro with Retina DIsplay. The TV has a VGA and an HDMI port, and I have both cables (VGA-VGA and HDMI-HDMI).

All I'm missing is a thunderbolt-VGA or thunderbolt-HDMI cable, and I can't decide which one to get.

Basically I'm interested in greater video quality, but I'm not sure if the TV is able to display the superior quality of HDMI video. I think it's a Full-HD TV (1080p).

So, my question is: would the HDMI cable provide the TV with actual better images? Would that make a difference considering the Retina Display?

I'm also worried about the possibility of needing to connect the macbook to a projector, as those usually still have VGA ports. (Or is that changing?)

Thanks for the advice (:

Alessandro