Summary:
Yes, there is. When it comes to HD videos, higher resolutions and refresh rates, VGA could be problematic and provide degrading quality. Also, remember that VGA is analog while HDMI is Digital. Analog to Digital conversion is def an overhead and cause signal loss no matter how good the A-to-D circuit is.
[Edit] As @ClosetFuturist said if you are not that much of a video geek and a hardcore graphics person or gamer, you might not notice that much of a difference in quality and VGA could be 'just fine' for your needs.
Narrowed-down Literature:
VGA
VGA or Video Graphics Array is the oldest known display connectivity option for computers and there are hardly any computers without it. The signals are analog and transfered as 3 different colours over 15-pin sockets. Everything is analog and there are no complications. VGA supports resolutions upto 2048×1536px @85 Hz which well covers the Full HD range. This option is the most simplest connectivity everyone uses to connect pc’s to LCDs but since its analog, its definitely not the best in quality. VGA carries only video and no audio and needs additional audio inputs to your lcd receiver for sound signals.

HDMI
HDMI has been around for quite a while, but its only since the past 2 years its been quite common around us making their appearances on LCD’s, mobile phones, laptops and tablets. Due to its full digital nature, the quality is outstanding and the best in class in today’s video options. The connector sizes are very small compared to VGA and DVI and also carries audio making it more of a multimedia connectivity option compared to a video only option. The most widespread application is for the connectivity of Full HD signals to a Display from Blu-ray players, laptops and gaming consoles. HDMI supports a maximum resolution of 4196 x 2160 which is higher than what would be needed by most.

HDMI is backward-compatible with single-link Digital Visual Interface digital video (DVI). No signal conversion is required when an adapter or asymmetric cable is used, and consequently no loss in video quality occurs. So this makes it clear that DVI and HDMI are electrically the same, but still then, why HDMI??
The Final Verdict
Clearly digital is better than analog, so VGA is out of the game with pure analog signals, bulky connectors, video only outputs and chances for interference. Among the digital options, HDMI and DVI has electrical same video signal properties, but the point where HDMI wins clear cut is that HDMI is found on mostly every HD device available today, has very slim and easy to use connectors making it the most user friendly connector and the best of all, transports audio along with video on the same cable! Chances for interference are very less with good quality cables, so make sure you buy Category 2-certified 1080p cables with the shortest length you need for the best quality. So if you have either a pc, laptop, tablet, mobile phone, HD gaming console or even a DVD player, HDMI is the best multimedia connectivity option today for anything compared to DVI and VGA!
Source of Full Article
answered
Aug 02 '12 at 19:55
TjWallas
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