5e spells suggest a way to mechanically differentiate what Champions calls Killing Attacks from Normal Attacks. The 5e spell Sacred Flame auto-hits but allows the target a saving throw to avoid damage. Fire Bolt requires a to-hit roll that determines whether or not the target takes damage. Since the latter is the normal D&D mechanic for determining death of a target, that will model the Killing Attack, and the auto-hit/saving throw will emulate the normal superhero combat mechanic.
This allows for an interesting mechanical smorgasbord in terms of attack and defense. Each attack power gets to specify which attribute is used for a saving throw:
It also gets to designated what type of damage it does:
Defense would include Resistance to the various types of damage, Damage Reduction for various types of damage, and the good ‘ol Armor Class.
This leaves a huge (maybe even too big?) amount of space for players to come up with all kinds of weird ways to explain why a Lightning attack targets Charisma.
Alternatively, the type of damage could pre-determine what kind of saving throw is required:
Strength: Cold, Fire
Dexterity: Bludgeoning, Piercing, Slashing
Constitution: Acid, Poison
Intelligence: Lightning, Thunder
Wisdom: Force, Psychic
Charisma: Necrotic, Radiant
Note how the latter limits choices on how special effects function and how arguments can be made why one type of damage also belongs with another type of saving throw...which is why I hesitate even though it would make things "easier" mechanically.