While the difference between them is obviously far less than the difference between a fighter aircraft and a space vehicle, there is at least one documented case of one of these
shooting down one of these
in Viet Nam. It was not a fair fight of course; the A1 caught the MIG 21 by surprise. Still, it happened.
That being said, I have a hunch that we don't run into space aliens all the time because of one thing: >Speed of light travel may not be possible. Notice I said "may" not be possible; I'm not saying it is for sure impossible. But with all the planets out there, and the probability that there are many technological aliens, you would think that we would have really solid evidence if interstellar travel was common. Unless space is just too big, and we are in for a real big surprise someday when they do get around to us...
have you ever read any of the terraforming novels by guys like niven and silverberg and thought about them against the mythos of the world?
in the judeo-christian canon, there are a number of spots, notably enoch, elijah and jesus's ascensions, the ark, the thing described in ezekiel and all shot through the fragments of every body else's mythology, that scream interstellar travel by planet builders at me.
if hyperlight travel is possible for these advanced races, which are not necessarily hominid, the time it takes to get between here, home and back in ship's time versus planetary time, equates to thousands, possibly even millions of years for distant home planets, by the lorentz time contraction calculation.
arthur clarke hit on that in childhood's end by having our guardian race turn out to be red-skinned and horned with a tail..
the most plausible explanation that presents itself to me is that the immortal pantheons of the norse, greek, hindu and whatever else i may be unfamiliar with, actually had some basis in reality and the stories have become distorted through time.
something went down that compelled the galactic management to shut off access to the planet because of violations of approved planet building and population control procedures, leaving us to our own devices to sort it out.
by everything i've been able to glean, we aren't going to see them for sure until we either demonstrate that we're worthy of re-admission to the galactic confederation or are on the brink of wrecking the planet's surface again.