No, they are different spell effects.
A lot of spell effects will say they work as another spell, but thats for the sake of being brief on the description, ease on the rules, and save physical space on the books.
Imagine if each summon monster spell had to repeat all the rules, but add more monsters to the list that you could summon. We probably would have a whole chapter on the core book dedicated to those spells.
When the spell effect says "you gain the benefits of (...)", we are ignoring everything on those spells (range, target, duration, school, casting time, etc), except for their actual effect (more specifically, the benefits of the effect), and apply to our spell effect.
A Mythic Spell is not different spell from the non-mythic version. And you don't have to learn both versions separatedly (if spontaneous caster) or prepared a different spell (if prepared caster).
These spells aren't separate spells you gain as a spell known from your spellcasting class, but rather mythically charged versions of spells you already know.
But nothing on the mythic rules says we can apply mythic spells on the effects of other spells. On the contrary, it says the spell effect does not change unless the text on the mythical version says it changes:
Unless a mythic spell's description says it improves, replaces, or upgrades an effect of the non-mythic spell, or says that it creates an effect instead of the non-mythic spell's effect, it retains all the effects of the non-mythic spell in addition to the effects of the mythic version.
So, our Mythic Guardian of Faith would have to say:
- The target gains the benefit of mythic shield of faith and your choice of mythic protection from chaos, evil, good, or law.