Daaaaamn the mangaka changed the fight.
In the LN, Ed lost the battle because he decided to take the hero's special move head-on (as opposed to dodging it) because there were civilians behind Ed who would have died if he didn't deflect the slash. Little did he know, Tia (the elf) had set up a barrier to protect the civilians...anyway, this was supposed to be the first time Ed demonstrates his willingness to sacrifice his personal gain for the sake of doing good in the world, particularly for strangers. This is an important aspect of his character, which is expanded on in subsequent adventures in the LN.
It's a shame the mankaga changed this scene in such a way to exclude that element of Ed's personality.