There's no difference - I don't want to punish players who aren't engaged with the battle system, so they can skip it with no downside (other than that it defaults to a HP win so you don't get to see WP or Shatter win dialogue screens) :)
The Hall of Fame runs on the honour system, but if you want to show everyone that you definitely didn't use autowin then a WP win will do it. Hall of Heroes is impossible to get into using autowin, obviously.