The one in the photo on the right looks more like my pullet. I have a plan for breeding her. I have a gorgeous barred bantam cochin roo so....the plan is to breed the blue pullet with not so great barring to the roo to clean up the barring. Male offspring will be bred back to her. This will maintain the barring and give me a split blue gene. Then the male offspring from that mating will be bred to blue or splash hens which will give me all barred chicks that are either blue or split to blue.
I only know this because someone who knows more about poultry genetics than me worked it out!
if you breed a blue barred to a barred, you are going to get both blue barred and barred. The barred will not carry or be split for blue as blue is dominant.
When you breed the male offspring back, blue barred to a blue, you are going to get splash, blue and black barred (I honestly do not know what a splash barred would look like though), and the same blue barred bred to a splash hen you are going to get splash and blue barred. Of course in all these breeding non barred in the same colors are possible too.
The only blue gene that you can say your birds would be split for (in laymans terms carrying) is self blue, AKA lavender. This is a recessive gene and works a whole lot different that the Andulusion blue gene.