This is a phenomenal gap. A.J. could strike out his next 110 trips to the plate and still be way behind the Big Breeze, who by then would have piled on a fresh batch of 30 Ks or so, since he's not one to rest on his laurels. Dunn probably has more categories of strikeouts than A.J. has strikeouts: swinging and missing, foul-tipping, caught looking, caught yawning, caught belching....
For A.J., striking out is one of those events, like getting caught in the rain, that happens periodically no matter how you try to avoid it. For Dunn, striking out is just something you do three or four times a day, like eating a meal.
A.J. clearly has a mortal fear of fanning. With two strikes, he protects the strike zone like it's one of his children. He shortens his swing and goes the other way, and often gets enough on the ball to bloop it into the outfield—one of the reasons his average (.284) is 121 points higher than Dunn's. When the Big Breeze has two strikes, it's the same old colossal all-or-nothing swing. When you've fanned 1,762 times in your career, it's lost its chilling effect, except for those around you. Instead of fearing failure, Dunn may be hooked on it.
This brings up an obvious solution to the Adam Dunn K problem.
A.J. doesn't really need three strikes each at bat. Dunn could use an extra one. A.J. should give one of his allotted strikes to Dunn. Under this plan, it would take two strikes to whiff A.J., and four to fan Dunn.
Now, it could be that even this wouldn't make a difference. A.J. probably would be tough to fan even if it only took two strikes. And the Big Breeze might keep a blowin' even with four. But my gut says Dunn would be a terrific hitter with a 3-3 count.