There's a thread on the other situations that could happen depending on who you battle at Yureyu and then if you choose to go upstairs or stay down. I'll try to see if I can find it, unless somebody else knows?
EDIT: Found the results:
From this thread, if you want: http://www.pokemonreborn.com/forum/index.php?showtopic=13622
Fighting Sirius at Yureyu and then staying downstairs with Sigmund reveals the two major character backgrounds, making it the "correct" choice. (Really, there's nothing affected story-wise, but this choice is the one that tells you the most.) The characters would be: