I didn't want to post math because most people on this board don't actually understand how the game works. For instance, Skill + STR/2 = Attack. Dancer and PUP start at the same skill level and Dancer has more STR than PUP, so Dancer has higher attack before considering gear.
If you think of a potential STR/Atk Kila +3 offhand, I think it's safe to say that Dancer has at least as much attack as PUP and likely about the same STR. PUP gets more STR on their AF3+2 than Dancer does, but Dancer starts higher and gets 10 from their offhand. If DNC doesn't want to offhand a STR/Atk Kila +3, it's because something else is more beneficial to them. That's flexibility that the PUP doesn't have.
Verth is D35/+51 Delay and PUP starts with 340 delay, but they have PUP pants +2 which are -10 delay. They have 376 base H2H skill, 16 from merits, 5 from AF3+2 head, and 7 from Faith Torque. This gives them 47 base H2H damage.
(35+47)/(340+51-10) = 82/381
Assuming Epona's, Atheling, Twilight, AF3+2 head, and Brutal, PUP/WAR is looking at 3% TA and 26% DA, or 1.312 attacks per fist. If they have 25% Haste, then they're only swinging with 75% of their delay. People say it's 60 delay per second. It isn't quite, but we'll use it. Also, there are 2 fists.
60*2*1.312*(82+fSTR)/(381*.75) = PUP DPS
Dancer with Twashtar/Kila +3, 25% haste in gear, AF3+2 body/neck/Suppa, Atheling/Twilight/Epona's/Brutal/Saber Dance, and Haste Samba has:
3% TA and 34.5% DA: 1.395 attacks per dagger
30%+5%+10%+3% = 48% Dual Wield
25%+10% = 35% Haste
60*1.395*(45+fSTR + 48+fSTR)/(366*.65*.52) = DNC DPS
@fSTR=0 :
PUP DPS = 45.2
DNC DPS = 62.9
DNC divided by PUP = 1.4
@fSTR=4 :
PUP DPS = 47.4
DNC DPS = 68.3
DNC divided by PUP = 1.44
@capped fSTR= (12 for PUP and 13 for DNC)
PUP DPS = 51.8
DNC DPS = 80.5
80.5/51.8
DNC divided by PUP = 1.55
PUP has an effective delay of 190, or 5.2 TP/hit. They hit 1.312 times per fist, and swing a fist every 142.5 delay. 60 Delay per second.
60*5.2*1.312/142.5 = 2.87 TP/second before STP
DNC effectively has 95 delay per hand with this setup, meaning they hit for a base of 4.2 TP/hit. They hit 1.395 times per swing, and swing once every 62 delay. Again, 60 delay per second.
60*4.2*1.395/62 = 5.67 TP/second before STP
DNC TP Gain / PUP TP Gain = 1.97
In the worst case scenario, Steps and Reverse Flourish don't help Dancer and they shouldn't use them. In that situation, the Automaton would have to provide benefit equal to 40-55% of an Auto-less PUP's melee damage and 97% of an Auto-less PUP's WS damage.
Looking back over this, I notice I neglected Verth's 15 STR and critical hits in general. Whatever, PUP has the first and Dancer likely has more of the second (along with crit bonus). Accuracy is kind of a non-issue, because the two jobs are roughly equivalent. PUP gets a ton of Acc on their AF3+2, but Dancer gets traits and Closed Position (50 Acc). Dancer gets about 10 more STP in their ideal TP set, if you're wondering, so they actually get TP more than twice as fast as PUPs.

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