Well more org to tanks still help, it may mean you can get by with using less infantry and more tanks. You also get large increase in tanks breakthrough value which may make attacks much less costly.
I'm definitely not questioning the breakthrough stuff. However, it looks as though the branch bonuses were decided before units went through a major balance change. The armor org bonuses used to be significant, but now that Inf are the main sources of org and hitpoints, they are rather. Moreover, they can't really increase the armor org bonuses without breaking their new balance scheme. For any reasonable armor division composition, +15 inf org is going to just be straight out better than +3 tank org.
If you look at the mobile infantry versus blitzkrieg branch, on the MI side you've got: +0.2 recovery (inf), +10% speed, +28 org (+25 mobile inf, +3 tank) and +10 org to your non-mobile inf divs. On the blitzkrieg side, you get +0.2 recovery (tank), +20% breakthrough, +11 org (+5 mobile inf, +6 tank). If armor divs are half-half (and I think that's generous), then the recovery cancels and going from MI Blitzkrieg is trading +10% inf speed and +17 org (and +10 org for inf divs, which would be the majority) for +20% breakthrough. It seems off.
Keep in mind that breakthough only matters until you have enough to counter the enemy, and armor divs already have a lot of breakthrough, so in a lot of situations the additional +20% won't have any effect.