The monitor connected via VGA should display a worse picture/color quality than HDMI simply because VGA-Display Mode officially supports 256 colors instead of the approximately 1 billion colors possible in HDMI v1, but as pointed out to me it is possible to use true-colour in 24 bit mode.
The response time should also be lower because VGA supp0rts 70Hz and HDMI v1 can support up to 120Hz. I wrote should because most monitor manufacturers limit the HDMI response rate to 60Hz, but this is entirely dependant which monitor, HDMI cable and GPU you use.
You should look up which HDMI version your graphics card and Monitor supports. Standard is HDMI v1.3 or higher. You should also check if your graphics card support three monitors at the same time (two external and laptop display).
All that aside as this was purely technical stuff. You may not even notice the difference between the HDMI connected display and the VGA one. I personally have both connected to my PC and I really don't notice a difference, but that is also dependant of your cable and display quality.