Lets start here:
Yes you can.
The enmity generation (all enmity listed as enmity potency) of a proper warrior opening (infuriate -> unchained -> Heavy -> Berserk -> Skull -> BB -> Heavy -> Maim -> Path -> Heavy -> Skull -> BB) is 14,953 (we're timing out berserk real tight here to get that last BB out just before pacification hits, and might lose around 1000 enmity if we're sloppy at all, but even at 13k ePot this still all checks out) over that 20 seconds. A paladin in sword oath will put out, in that time doing FoF/CoS timed to get two in and dropping Spirits Within on CD (only once in the first 20s, granted) hits 7,106. That's less than half and assuming the paladin is not holding back at all.
After that initial 'wee all my CDs' spike, as a warrior using path every two BBs (enough to keep it up), and only using eye situationally (as you should), you'll be generating 3,290 enmity per combo, on average. A paladin, who is still not holding back, is going to be producing 1,887 in sword oath. IF you decide to keep up eye all the time for some reason, you'll still be keeping up 2073 enmity (give or take a couple tenths), which is still about 200 more per combo than the paladin and more than enough to keep your loldoubleyourenmity lead.
Note: I'm not calculating in the slash resist debuff, only berserk, unchained, FoF, and maim, because pld and warrior will benefit roughly equally from the debuff (warrior will actually get a bit more out of it because CoS and SW aren't slashing but whatever).
So, yes. Yes you can keep aggro. Easily.
Now, moving on:
A war who is off tanking's maximum damage is to just spam BB, popping berserk when they can and keeping fracture up. This isn't what you'd actually do because, as you said, the path/eye combos are great and you'd probably be keeping them both up to keep enmity down, but lets just look at what a warrior can do in berserk. You've got enough time for about 2 combos + another attack. So that's 150, 200, and 280 potency x 1.50 x 2 and then a fracture snap casted at the end. Or, 1890 potency in those 15s plus another 450 over the next thirty. Probably tosses in a brutal swing during berserk for an extra 75 potency. So altogether, we'll just say 2415 (possibly 2715 if we time berserk just right and manage to drop a skull sunder before our snap fracture) potency in 20 seconds (15 of berserk, 5 of pacification)
Meanwhile a paladin is doing FoF for 20 seconds, and dropping two CoS in that time, along with 3 rage combos, and a spirit's within. So that's 100 + (30 x 5) x 1.3 (fof) x 2 for the circles which is 650 potency from the two circles, plus another 300 for spirits (I don't believe this gets the FoF bonus as I believe it's magical), so that's 950. Now we add the three rage combos, which are 150, 200, 260, added up that's 610, multiply by 3 because we can do this 3 times, and it's 1830, multiply by 1.3 for Fof and 2379, add the circles and spirits and that's 3329 potency in 20 seconds (180 potency, admittedly, will land via the second snap casted CoS in the five seconds after that, but 3149 is still more deeps than an unstanced war).
Now let's also add that you're going to get about 8 auto attacks in in that time as either, BUT the paladin in sword oath gets +50 damage on each.
So the paladin is hitting, with buffs up 3329 potency, plus another 400 damage (straight damage, nothing really impacts that other than weapon speed) in the 20 seconds they have their primary damage buff up, while the warrior is hitting 2415 with no added damage.
Add in that the Warrior is taking hits to potency to put up path, if not both path and eye, and well it's pretty laughable that you say the warrior can drop defiance to do nice damage and the paladin can't.



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