Longer ATA means the bow is a bit harder to move around (both tipping side to side, and front to back) which makes it " jump" less along those planes when shot (But can jump forward as much as any bow...Not that that would be a problem as this occurs AFTER the arrow is gone.)
Short brace, as mentioned, means the arrow is on the string for a shorter amount of time. I also question how much this really effects the shot...at least on a NON drop away rest, as the arrow is still in contact with the bow. Another thing the short brace does, is it amplifies any imperfections in center shot and nock height.
Lay an arrow on the table, with a pencil under the arrow at the tip. Doesn' t look too bad...now, while holding the nock down...slide the pencil back to the nock. Suddenly the tip of the arrow is 12" in the air. Think of the pencil as your arrow rest, the closer to the nock (string) the more pronounced the imperfections will be...and that INCLUDES imperfections due to a poor follow through, or torqueing the bow. Drop away rests shine best on short ATA and brace bows.