Harmony - Troop Symmetry

I don't understand what the difference is at all; in both cases, I ran, killed the neutrals, and won the final battle. Where did these "different strategies" come from?

Describing different game situations is not just a matter of a few words... I won't take that on.

For example:
It's not always beneficial to attack immediately. Sometimes it's more profitable to play by buying troops: gather troops, defeat a neutral unit, and you're in the plus. And sometimes: invest money in development, and you're in a bigger plus than from the bonus for killing a neutral unit.
You want to increase the benefit of one solution – attacking.

Added 4 minutes later

I'm also curious how the Guardian was supposed to function for the Seraphs, considering that for it to work, the entire hero's army must be dead.

It should work as a single cast per battle on a selected unit. The unit dies – a part of it is resurrected (depending on the strength of the Seraphs' stack)