I was intrigued by the comparison of new math and Common Core math, particularly by the breaking up of the multiplier into factors. It does beg the question of how they would handle 23 x 17 = ? I believe the old-fashioned way I was taught would handle all situations and all sizes of numbers.
Additionally, breaking the multiplicand into differences is something the students will learn in algebra, so it is an unnecessary complication in early grades. They also will learn to factor in algebra. Again, there will be a large number problem.
It seems to me that Common Core is publish-or-perish chicanery and should be stopped now. Your comparison demonstrates that effectively.