The point is not that using the dagger does more damage. It's the noise that you make. It's nearly impossible to sneak up on someone using one-handed two-handed weapons because they make noise. Daggers don't make any noise when sneaking.
This is a fallacy. It's more dependent upon your Sneak level along with the types of enchantments you have on your armor/weapons. I have a Dunmer Assassin in full DB armor with muffled boots and a plus %25 sneak ability hood and necklace. I am also level 72 in Sneak with 8 perks including: Stealth (2), Muffled (1), Backstab (1), Deadly Aim (1), Light Foot (1), Silent Roll (1) and Silence (1). It is
extremely (I say that with the utmost importance) rare that I am ever spotted. I use a dagger and a "special" daedric mace.