True dwarfs are smaller, have rounder bodies and heads, and make better show bunnies.
If you breed two true dwarf rabbits together, you will get (generally), 50% true dwarf, 25% false dwarf, and 25% peanuts.
What are peanuts?
Peanuts are babies that inherit two dwarf genes. They lack the proper gene to grow, so they wither away within a few days. They basically become TOO dwarfy. They will always die.
This is why I like to breed false to true. You get the same amount of true dwarfs, on average, which is 50%. And that way, you have a higher percentage of all the babies in the litter surviving; you have a higher chance of no fatalities.
I'm planning on showing my little show does, like Cinnamon, once she comes off her litter, and one of Cinnamon's daughters that I plan to keep. Sure, I don't have a buck that I can show, maybe he can't win any legs (awards), but I'd rather have that than 25% of babies that will die per litter.