Suppose both characters are killed by some kill effect (i.e. Die by the Sword).
"If The Hound is killed, place him in your discard pile instead of your dead pile."
"If Aeron Damphair would be killed, instead search your deck for...and put Aeron Damphair on the bottom of your deck"
Does "would be" prevent Aeron from actually enter a moribund:killed state, or is he still considered killed in Step 3 and doesn't become moribund:bottom of deck until Step 4?
Also, if you're not the owner of Aeron or The Hound but control them, that doesn't affect their moribund replacement effects, right? That is, the terms "your" doesn't change the effect. So they could be read as:
"If The Hound is killed, place him in his owner's discard pile instead of his owner's dead pile.
At the beginning of the dominance phase, discard the top card from your deck or discard the Hound from play (cannot be saved)"
"If Aeron Damphair would be killed, instead search your deck for a non-unique HOLY character with cost 3 or lower, put it into play, shuffle your deck and put Aeron Damphair on the bottom of his owner's deck.
