displays that have more than one input, have usually a button called SOURCE, which changes between which cable it uses to display things.
Connecting both will accomplish following:
your computer will see two copies of same screen, one for HDMI other for DVI/VGA
Thus you could have two desktops, from which you see only one at a time.
pressing said button changes which cable screen uses to display image from computer.
It will not hinder or make display work better since screen cannot use both at the same time.
As a side note, there is no big difference between HDMI and VGA if you are at 1080P and 60Hz, going to higher resolution/refresh rate can change things.
HDMI cable can be faulty/have bad connectors, same goes for GPU/display which can be a reason why it loses connection at times, this can pretty much be tested by using same cable on another setup to see if it works there or not.