the responses to the original question point to several ideas for
listening.  Oddly enough, I discovered that the only two versions of the
variations I have in my collection are both by Russians:  Nikoleyeva and
Gilels.  I really need to get hold of the Brendel version.

The interesting thing to me about this particular set of variations is
that it is unusual in having a long introduction --almost a sonatina of
sorts--introducing and developing the theme.  A brief simple restatment
of the theme follows, which is where most variation sets would commence.

There follows the expected series of variations.  However, the work also
concludes in unconventional (and wonderful) ways.  The fifteenth variation
is an extended largo in the key of EbMajor which will be the home key
of the Eroica Symphony completed two years later.  This variation of
roughly 3 minutes is followed by a briefer coda.  The piece then concludes
with a fugue; in my limited experience, I don't know of other Variations
that use four and a half minute fugues (as opposed to canons).

The reason for the description above is to set this work and, of course,
the Diabelli Variations, in contrast to most variations, including others
written by Beethoven.  At their best, a set of variations takes a fairly
simple (or, as with Diabelli's ditty, banal) theme and then turns it
around in a variety of ways that shed light on it--generally increasing
its interest to the listener.

Beethoven often wrote variations on commission and quickly.  I can't
help but feel that his skill as an improvisor helped him with this and
that had he lived 150 years later, he might have been using his skills
as a jazz pianist--jazz piano being, in significant ways, the creation
of a series of variations on a common theme.

Horowitz admired the great jazz pianist Art Tatum.  I heard a story
(likely appocryphal) that when they met Horowitz played a short piece
for Tatum that he had composed in his honor.  And that, then, Tatum sat
down and improvised on it for twenty minutes!

This is by way of raising the issue of what qualities distinguish a set of
variations that are truly "art" from those that are "mere" entertainment.
How are the Eroica Variations or the Diabelli Variations "better" than,
say, Beethoven's own earlier efforts.

 From my limited listening to the two Russians, I far preferred Gilels.
I felt he told a story of the growth and development of a hero.  In
the introduction, the theme seems to sneak out from between the massive
chords, growing in stature as it develops, them going through a number
of challenges (variations) before emerging in heroic fashion in Variation
XV in its full maturity.  Perhaps, this vision is inspired by familiarity
with the Symphony to come, but I felt Gilels did a wonderful job of
providing a sense of "unity" to the variations.

Ed