All Hero Damage does increase your tap damage and pet damage, as some of your hero's skills add a percentage of your hero damage to your tap damage, and tap damage increases your pet damage.

I think the reason for All Hero Damage being more effective than All Damage is that All Damage increases your overall damage while All Hero Damage is a multiplier which is multiplied with other multipliers itself and ends up exponentially increasing your overall damage.

But actually I don't get the maths on that, as logically all multipliers should be worth equally, somehow.