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Both are at their strongest and Aang has no problem with killing Eragon and Saphira. This takes place in two rounds on Aang's world.

1. Normal Aang
2. Avatar State Aang

Who wins each and why?

Aang has homefield advantage, but unless you take away Eragon's 12 death spells, it's pretty unfair. I'd say Saphira is more maneuverable than Appa, but not more maneuverable than Aang on his glider. I know for a fact AS Aang wins. First fight is a bit more difficult to guage. I think though with his multitude of fighting skills and massive variety of attacks, he can wear down Eragon's shields and just work him over until he wins.

Avatar-verse has a clear distinction between the physical world and the spirit world. Are we working under the assumption that Eragon's magic functions the same in Avatar-verse?

Eragon wins both by popping a blood vessel in Aang's brain.

I think Saphira would Eat Appa and Eragon would beat Aang with his magic.

AS Aang would win but Appa still gets eatten. Mmm Appa Chops.

Eragon's magic works as perfectly as it does in Alagaesia.

Do either combatant have any prior knowledge of the other?

No. I would have said if they had.

Originally posted by jmoul
No. I would have said if they had.
Your supposed to say if they didnt as well.

But I stand by my claim.

Eragon/Saphire win but Aang wins with AS.

With no knowledge, I don't see what stops Eragon from death spelling Aang in both states, except for maybe Aang's raw power.