Everything here is done without armor and accessories just the weapons involved.

Normal Weapon Damage Output(a single SKILL attack 10 times)
1972 pts sword highest: 320 lowest: 129
1578 pts daggers highest: 302 lowest: 116
Conclusion: Sword has more damage

DOT(20 secs) without buffs
998 pts Sword crits: 2
1193 pts Dagger crits: 6


DOT(20 secs) with increased crit buff(Poma wine herb dumpling used)
1384 pts Sword crits:10
1343 pts Dagger crits:10

NB: The above results suggest that upon delivering an equal
number of crits and whatever base damage is done both weapons deliver relatively
the same amount of damage.

However on further detailed inspection through the use of trials considering crits ALONE the following results came up:

DOT Crit Trials with poma:
Trial 1 - Sword: 10 crits Dagger: 10 crits
Trial 2 - Sword: Zero crits Dagger: 10 crits
Trial 3 - Sword:8 crits Dagger: 12 crits
Trial 4 - Sword:8 crits Dagger: 8 crits
Trial 5 - Sword:4 crits Dagger: 8 crits

NB: The above results suggest that under the influence of more crits the dagger has approximately twice the chance of inflicting critical damage. This suggests that with crits the dagger is superior and will inflict more damage over time than the sword.
Remember on the 1st trial both weapons recieved an equal number of crits and were both proven to inflict relatively the samedamage. So since the dagger is proven to have a greater chance of crits which does
almost twice the damage of normal base damage the dagger will definitely be superior. But we all know this.
The real question is how superior the dagger is to the sword over
a given time.
Remember in combat an assasin can run out of skills to use and may rely on the normal non-skill attacks. The answer to this question will help you to decide which weapon is best under the influence of crits on a rainy day.

The math (forgive if incorrect):
From trials above total number of sword crits above is 30 crits and total dagger crits is 48.
Therefore 48 - 30 = 18 crits difference between dagger and sword
Therefore percentage of extra damage a dagger will provide as opposed to sword is :
18/48 = 0.375 * 100 = 37.5 % extra damage

Now who wouldn't want that :D

Remember the dagger is inherently faster and will therefore have a greater chance of landing more crits

BUT ...

This test could swing other ways

What if you've reached endgame and already have over 1000 crits with food etc. wouldnt you take the Sword for the extra damage and godstone procs provided that adding more crits is useless AND MORE IMPORTANTLY from the results above, both dagger and sword are proven to deliver relatively equal damage when the crit rate is the same.

To assist with this discussion if any of you know the current max crit points needed plz post below to show the possiblility of obtaining that max crit level before even deciding to buy a dagger or sword.

From my simple test the sword could be more superior to dagger since sword's godstone may have greater chance of proc while the damage of both weapons is about the same.