Conclusion - Having stated the three above sets of parameters
for the above three types / shapes of Antennas that are often
used as In-the-Attic Antenna : It now becomes apparent to me
that the Loop Antenna is the better choice with a potential for :
* Higher Signal Levels due to the fact for the available space
there is simply more Wire in the Air.......................................

This can vary though. Would depend on the bands used, etc..
Just having more wire in the air doesn't mean much in itself.
It's quite possible and common for a smaller footprint antenna
to trounce the larger one. IE: my coax fed dipoles have a total
of 440 ft of wire in the air. Yes, it works well on any HF band,
but my yagi would eat it for lunch on the bands the yagi is designed
for. And the yagi uses a total of appx 90 ft of element/s to do it.

* Equally as low Noise due to the natural properties of a Loop.

And what would these properties be? The only "noise" property a
loop has that differs from any other wire antenna is the reduction
of corona, or static buildup, etc. And only in locations where that
could help, would it be any advantage. Here in Houston, it would
mean nada. At HCJB, with the large amounts of element eating
corona up in those high mountains, it can help. Other than that,
the loops behave no different than any other antenna.

* Greater Antenna Aperture {Signal Capture Area} due to the
natural shape and size of a Loop in any given space; with less
apparent signal fading.

This means little in general.. I can run a full wave loop on 80m
for NVIS, and compare it to a dipole, and they are almost exactly
the same in the real world. If you model a 80 dipole at 40 ft and
compare it with a 80 horizontal loop at 40 ft, the loop has the small
advantage of 1 db. In the real world, this is basically unnoticable
on HF. It's not the aperture you would want to worry about.
It would be the pattern of the antenna on the various bands, vs
whatever you would compare it to. This can easily be modeled.

Going One Step Farther : A Vertical [Tall] Loop Antenna
In-the-Attic could offer almost as many advantages over the
Random Wire Antenna and Dipole Antenna; as does the
Horizontal [Flat] Loop Antenna.

You say? What would these advantages be? Have you tried modeling
it? You might be surprised...
A full wave loop has no advantage over a dipole, except in differences
in
pattern. They are both about equally efficient.
What would that mean? On some bands, the dipole could be better.
On others, the loop... Basically, it's a crap shoot.
Here, I have enough room to run either full wave loops, or dipoles.
I run the dipoles. Why? Same appx performance, with less work
involved. On the higher bands, I'd generally prefer the dipoles, vs
a horizontal loop due to current distribution concerns.
Vertical loop vs dipole? About 2 db or so, and barely worth the
trouble.
I'd rather run an extended double zepp, vs the vertical fed loop.
Has about 1 db more gain on it's design freq.

Intuitively I would
think that for a Vertical Loop Antenna to perform up to its
potential the maximum Length-to-Height (Aspect) Ratio
would be about 4:1 or 5:1 .

Nope. The maximum performing loop is a perfect circle.
A square would be better than a tall narrow loop. Whatever
covers the largest area is best as far as gain.
If you want horizontal, you feed at the top or bottom.
Vertical, from either side.. A loop is a loop no matter
the orientation. Same properties will apply to both.

Anyway, there is no real advantage to a loop vs dipole, unless
the pattern of the loop is more favorable for a certain
band and direction, etc, in use at the time. This will vary.
As far as s/n ratio, you could run either one with little or no
difference on most the bands, assuming both are properly
decoupled from the feedline..
MK