Non-Template based Creature Type Changes

[Vespero]

This is a question that I've come up to and tried to figure out, but I can't.

What happens to base attack, saves and hit dice when a creature changes types without receiving a template?

Example 1:
I'm running a campaign with a Planar Shepherd (I know, I know, rookie mistake. I don't regret it nearly as much as the Warmage. It's not so bad if you use base planes.) and at lvl 10, they become an Outsider. Does this change anything other than making them live forever and a pain in the butt to resurrect?

Example 2:
Arcane Hierophant. Augmented Familiars become Magical Beasts, does this affect past or future stats? I played one last campaign and kept leveling her as an Animal, but should I have done differently?

Thanks for your help.

[BowStreetRunner]

If the character had any racial hit dice, those would change. Class levels would not.

[Vespero]

If the character had any racial hit dice, those would change. Class levels would not.

So it would change for an Animal Companion, but not a character without race levels?

[Urpriest]

Since normal familiars keep their old RHD, Arcane Hierophant familiars should as well. Regardless, the bonus HD work differently, they are never modified because they aren't HD from a creature type.