The birds head grip sticks out further to the rear than a more vertical pistol grip. It is more comfortable to shoot, but it also keeps the length over 26". These are the crucial elements.
1. The overall length must be greater than 26". Essentially any combination of barrel length and grip length that results in an overall length longer than 26". The ATF arbitrarily decided that 26" was the cutoff. Shorter than that and it is deemed concealable. I think for marketing reasons, and the fact that Mossberg and Remington already made 14" barrels, it was decided that using the birds head grip with a 14" barrel made more sense than a shorter, more vertical pistol grip with a 15 or 16" barrel. No one really sees much of a difference between 16" and 18".
2. Don't conceal it. The definition of AOW revolves around concealable. If the barrel is less than the limits for rifle and shotgun, and it is concealable, then it is an AOW. Fortunately, the only defined characteristic for the class of weapons is the overall length. If they applied the standard of what a 7' basketball player could conceal under a duster, we'd be screwed. As an individual, if you conceal it, you the individual are the one in trouble. Not the rest of us.