Hey,
It's pretty much a coin flip.
I flipped a coin, it came up heads.
The order of operations predates the introduction and influx of abilities that can either add a character or enhancement to battle. The order of operations should be updated to treat play an enhancement abilities like banding abilities rather than like other abilities.
You get to play both cards (the one with Swift Horses and the one with Nebuchadnezzer) even if the first of the two removes the hero from battle.
Nebuchadnezzer has a search and an add to battle (band/play enhancement) ability. Search abilities are always paired (in this case it is paired with an add to battle ability) and search abilities follow the order for activating abilities of the ability they are paired with. Which means a search ability and the ability it is paired with will always activate together.
Tschow,
Tim "Sir Nobody" Maly