Wondering what the bonus type (if any) for these two abilities are and whether or not they stack with one another or if one supersedes the other.
From Ultimate Combat book, p.44:
Deflective Shield (Ex): At 2nd level, an armor master specializes in using his shield to def lect attacks. He gains a +1 bonus to his touch AC, and this bonus increases for every four levels beyond 2nd (to a maximum of +6 at 20th level); however, this bonus cannot exceed the sum of the armor and enhancement bonus to AC provided by the shield that the armor master is currently carrying. This ability replaces bravery.
From Mythic Adventures, p. 73:
Shield Focus (Mythic)
You’re a master of using your shield for protection.
Prerequisite: Shield Focus.
Benefit: Add your shield bonus and your shield’s enhancement bonus to your touch AC. As an immediate action, you can expend one use of mythic power to add your shield bonus and your shield’s enhancement bonus on a Fortitude or Reflex save just before you roll it.
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As written, they stack.
Deflective Shield (Ex) gives an unnamed bonus to touch AC, with a limit set by the total shield bonus to AC, but the bonus is derived from your class and archetype, not your shield.
Shield Focus (Mythic) gives an unnamed bonus to touch AC, derived directly from your shield bonus to AC.
Balance-wise, Mythic is Mythic, so you are in a different realm of power from the "base" rules and your opponents are, probably, in the same realm.
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I think the mythic ability is a shield bonus. It uses the term “shield bonus.” Although it could have been clearer it would have been awkward wording to write “Add your shield bonus and your shield’s enhancement bonus to your touch AC as a shield bonus and a shield enhancement bonus.”
But deflective shield seems to be untyped. I can definitely see a developer round table deciding to make it a shield bonus but the current wording doesn’t support that.
Summary: they stack.