All this mostly depends on how timely your reaction is to whatever's happening. Once you're a fair distance away, say the 21 foot metric of the Tueller Drill, against a bad marksman you probably have a pretty good chance; the average distance of gun fights as of some years ago was 7 feet.
for fair comparison you need to analyze most common scenario, which is multiple victims/targets vs single killer. it's going be day/night difference between dealing with a guy with a machete in his hand and a gunman...
I'm pretty sure the most common scenario is 1 on 1, or 1 on a few you're not willing to abandon, like SO or family, or multiple assailants, a small criminal "gang", on 1 or a few. The lone nutcase assault is very rare in comparison to normal crime.
If it's a few on your side you're not willing to abandon, it's entirely another matter and beyond the scope of our discussion.
If there's only one target, yourself, then if the one or more assailants are already within "critical distance" I personally don't think the difference between edged weapons and guns is "night and day", but I agree it's still quite big.
Review videos about the Tueller Drill (https://en.wikipedia.org/wiki/Tueller_Drill) and you may become less confident about your ability to try to escape an edged weapon.
All this mostly depends on how timely your reaction is to whatever's happening. Once you're a fair distance away, say the 21 foot metric of the Tueller Drill, against a bad marksman you probably have a pretty good chance; the average distance of gun fights as of some years ago was 7 feet.