So I figured out the reason unarmed was hitting for 0 damage - I had selected gladiator as my background and so I started with throwing nets, and throwing nets deal 0 damage.
Character: level 15 human gladiator with 17 str/dex. 11 fighting, 11 unarmed, 14 long blades. Note that long blades has an advantage here. Fighting against a yak:
+0 double sword
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AvHitDam | MaxDam | Accuracy | AvDam | AvTime | AvSpeed | AvEffDam
Attacking: 10.1 | 37 | 77% | 7.9 | 80 | 1.25 | 9.9
Unarmed
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AvHitDam | MaxDam | Accuracy | AvDam | AvTime | AvSpeed | AvEffDam
Attacking: 8.0 | 29 | 77% | 6.2 | 80 | 1.26 | 7.7
Roughly 20% less damage. Let's bump unarmed up to 14 to be fair:
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AvHitDam | MaxDam | Accuracy | AvDam | AvTime | AvSpeed | AvEffDam
Attacking: 10.1 | 42 | 79% | 8.0 | 74 | 1.35 | 10.8
Now unarmed is beating a +0 double sword. Let's crank up the quality of the double sword to +5 freezing.
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AvHitDam | MaxDam | Accuracy | AvDam | AvTime | AvSpeed | AvEffDam
Attacking: 16.5 | 58 | 78% | 13.0 | 80 | 1.25 | 16.2
About 50% higher damage when you have a high quality weapon. Let's increase unarmed to reach parity:
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_Increased Unarmed Combat to skill level 16.0.
AvHitDam | MaxDam | Accuracy | AvDam | AvTime | AvSpeed | AvEffDam
Attacking: 11.8 | 40 | 79% | 9.4 | 70 | 1.42 | 13.4
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Increased Unarmed Combat to skill level 18.0.
AvHitDam | MaxDam | Accuracy | AvDam | AvTime | AvSpeed | AvEffDam
Attacking: 13.6 | 48 | 78% | 10.6 | 67 | 1.50 | 15.9
Turns out it takes about 4 levels of unarmed to be equal to the jump from a +0 double sword to a +5 double sword of freezing.
For funsies:
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Increased Unarmed Combat to skill level 20.0.
AvHitDam | MaxDam | Accuracy | AvDam | AvTime | AvSpeed | AvEffDam
Attacking: 15.2 | 54 | 80% | 12.2 | 63 | 1.59 | 19.4
If you're willing to take unarmed to level 20, you'll deal more damage than you can with a (one handed) sword. All comparisons done without a shield, the shield should lower unarmed damage about 10% or so? If someone really wants to check they can, but it isn't terribly significant.
Wanna go grab 15 runes? Here's your endgame:
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_Increased Unarmed Combat to skill level 27.0.
AvHitDam | MaxDam | Accuracy | AvDam | AvTime | AvSpeed | AvEffDam
Attacking: 20.4 | 70 | 80% | 16.4 | 50 | 2.00 | 32.8
Good luck finding a yak in extended though...And you really should have trained more than 11 fighting by now.
TL;DR: With both at 11 fighting and 14 skill, unarmed is already doing more damage than a +0 double sword. But a high quality double sword (+5 of freezing) is roughly equal to 18 unarmed. Unarmed will continue to get better with higher skill whereas double swords are mostly maxed out at this point. Certain rare brands (vamp, speed, antimagic) may provide useful effects that unarmed can't quite duplicate (other than speed).