Chocobo breeding 101:

[Aphel]

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The only reason I can think of of why you would want to mate with a higher pedigree Chocobo (bought from NPC) is when you wish to retain those traits of your lower pedigree Choco. Say if you have a pedigree 2 Chocobo (3-stars in all stats, excellent ability like Dash, nice color) and rather then getting a randomized pedigree 2 cover and hope for the best, buy a higher pedigree partner (3 or above). That way it'll tend to use your pedigree 2 Chocobo's stats/ability for the fledgeling. Maybe....

Also, my previous Pedigree 3 Chocobo had 2 active abilities (Heavy removal and Chocobo Shock). That heavy removal ability, Chocobo Ease II I think, was hereditary.

As to whether higher tiered abilities have lower possibility of passing on to fledgelings, I have a feeling it's still 50%. This was what happened in my case:

Pedigree 2 (Dash I) + Pedigree 2 Cover (Chocobo Ease II) = Pedigree 3 inherited Chocobo Ease II, then later gained Chocobo Shock I at level 10.

Pedigree 3 (Chocobo Shock I) + Pedigree 3 Cover (Chocobo Shock II) = Pedigree 4 inherited Chocobo Shock II.