VE & CE cap at 10k each.
Assuming a level 90 target (since the generated hate for damage done is pretty much flat relative to mob level by that point), the rate of VE gain per damage is 240/61. I'm going to just treat it as 4:1 for approximations.
VE decays at a rate of 60 VE per second. 60 VE would be generated with 15 damage, so the decay rate is -15 DPS.
So, what overall DPS rate would cap VE in various intervals (after accounting for decay)? Looking at 10 second intervals:
265 DPS would cap VE in 10 seconds.
140 DPS would cap VE in 20 seconds.
100 DPS would cap VE in 30 seconds.
80 DPS would cap VE in 40 seconds.
How does that compare to potential damage rates? As my research primarily focuses on mnk, I'll use that to illustrate. (Note: this DPS assumes fairly aggressive playstyle.)
1. WoE empyrean (lower tier weapon), haste, 2x march, full usu, bison steak, RR+SS atma: 280 DPS.
2. Lvl 85 fire Taipans, haste, 2x march, standard-good 75 gear (black belt, turban, byakko's, usu feet, etc), pizza, Stout Arm atma: 165 DPS
3. Same but without marches: 110 DPS
4. Lvl 80 fire Taipans, brown belt, ACP body, aurore pants, pizza, no notable atma: 80 DPS
Aside: Entry 1 is not fully top-tier. It's certainly possible to go well over 300 DPS, and that's even before adding Haste Samba.
So you can see that at certain points, DPS ramps up pretty quick. Of note, however, is that even the relatively weak 4th example will still cap VE within about 40 seconds.
Most NM fights will last 5-10 minutes, and the DDs are going to be capping out VE well within the first minute, often in less than 30 seconds.
On the CE side, the rate is 80/61, which means it will take 7,625 damage to cap out. Using the above sample DPS values, that will take about:
1. 30 seconds
2. 45 seconds
3. 70 seconds
4. 95 seconds
So aside from damage they take, it should take no more than 2 minutes, and quite possibly about 1 minute, to completely cap hate for a DD.
What is the pld managing in the meantime?
Assume he spikes hate at the start.
Engage. Sentinel, Divine Emblem, Flash, Rampart. 1800 + 3840 + 3600 = 9,240 VE. Assuming sufficient haste, a second Flash within the 30 second window of Sentinel for 11,800 VE, and subtract 1800 decay VE, you have 10,000 VE, capped.
Congratulations, you've manged to stay ahead of the tier 3 DD for ~30 seconds. Within 45 seconds VE becomes irrelevant, as everyone should have capped it by then. Provoke from /war is also inconsequential after that point, though it gives you a faster buildup at the start.
What about the CE side?
Two Flashes while under Sentinel gives you 900 CE. After that you're dependant on cures and damage done.
Cures: Kanican hasn't updated the data for post-75, but assuming it continues the same trend, the multiplier for level 85 should be 40/61, or 0.66 * Cure amount for CE. Assuming 400 point cures, that's 262 CE per Cure IV (before +enmity), or 2.98 CE/MP, compared to 7.2 CE/MP for Flash.
It takes 2.5 seconds to cast Cure IV, so you're getting about 105 CE per second. That's the equivalent of doing 80 DPS. So, MP efficiency aside, using Cure IV in a cure kit that interrupts melee is comparable to the damage output of the tier 4 DD.
Your other source of CE is direct damage. Since your cures are gaining CE at a rate of 80 DPS, your normal damage has to be doing at least that much as well just to maintain parity with the lowest tier DDs (well, lowest tier not-completely-gimp-idiot DDs).
The DDs are getting Haste and 2x March, so you should be getting the same (at least vs tier 1 and 2). If your group decides you're not worthy of a brd, there's pretty much no way to catch up.
Full Perle + Swift Belt should be considered base minimum, for 18% gear haste. Add 37% for total magical haste and that puts you at 55%.
I'll take out time for one Flash every 25 seconds, and one Cure IV every 15 seconds. I won't take out time for Utsusemi casting since I didn't remove that from the DD's DPS either. With the casting, you're using about 22.5% of your total action time, which means your damage is going to be reduced to 77.5% of its potential. Alternatively, if your DD potential is high enough, cut cure cast frequency in half and have 85% of your total time available for meleeing. I'll split the difference and just use 80%.
So, 80% of your damage potential has to beat 80 DPS, which means innate damage potential has to be at 100 DPS or higher. With 55% haste, your unhasted damage needs to then be 45 DPS or higher. It would be nice to reach 150 total DPS, which means unhasted DPS of 85.
In general, can expect weaponskills to represent perhaps 30%-35% of total damage, so melee damage should be in the range of 30-60 DPS.
What's needed to reach that threshold?
Joyeuse: 1.45 swings per round, d35 weapon. Max fStr: 11. If capped attack, max melee DPS: 37.5. Decently above the minimum, almost enough to reach tier 3.
Shamshir +1: d52 weapon. Max fStr: 13. If capped attack, max melee DPS: 35.5. Bit below Joyeuse; should have weaponskills that are about 20% stronger, but less frequent.
Of course that depends on capped fStr, which you'll probably have (depending on DD atma chosen), and capped attack, which you probably won't have (aside from maybe War, most full time DDs can't regularly reach the attack cap). Far more likely to drop to 3/4 of that at best, which is below the threshold for 80 DPS. That can be compensated for with dual-wielding rather than using a shield (somewhat dubius tradeoff if you still need a pld for tanking) plus minor +DA gear (ie: Brutal Earring).
Caveat: All that is rather sketchy, as I haven't run real numbers on things. It's also comparing against DDs going all-out, where they are more likely to be holding back, for !! triggers if nothing else. Essentially, with proper cooperation and focus it should be possible to barely stay ahead of the DDs for short periods of fights. A thf for collab makes this a lot easier (see anecdotes below).
Edit: Actually, I forgot that the 80 DPS DD isn't getting marches. That means that the pld *with* marches and atma is struggling to keep up with the low-end DD *without* marches -or- atma. The entire concept becomes more and more of a stretch.
Given that a pld can reach 2500 HP fairly easily in Abyssea, one should also consider CE loss rates. You're losing 0.72 CE per point of damage taken. Being hit for 364 damage removes 262 CE, the amount gained from a 400 point Cure IV. As long as you can fully cure your own damage, you can maintain a neutral hate level on CE, accumulating on damage done. However it's rare to manage that, as usually serious damage comes in large spikes that you'll want a whm with Cure V/VI to patch up (ie: 1000+ damage at a go); minor damage is blinked away.
What would fix things for pld? Well, one thing that would significantly alleviate it would be to change the tier 2 Guardian merit so that it was a 100% active trait, instead of only during Sentinel. Having it only active during Sentinel makes it a complete joke, unless you happen to have Sentinel up when you get hit by a huge nuke.
5 levels of Guardian, for a 95% reduction in CE loss, would mean that 1000 damage taken would only lose you 36 CE, a completely inconsequential amount (a shadow getting hit is -25 CE). At that point there's absolutely no reason to use /nin to conserve CE (may still want to use /nin for dealing with certain types of high-damage attacks, of course). Even if they downgraded it to, say, 15% per merit level, 75% total, that's still only 180 CE loss for taking 1000 damage, which can be made up for in a single Flash.
At that point you can switch to /war for the massive damage upgrade of Berserk and Double Attack, as well as being able to better take advantage of the Creed armor set.
Alternatively, could change Guardian to be exactly that requested trait: Raise max hate cap while Sentinel is in effect (say, +1800, which would allow VE to stay above 10k for exactly the duration of Sentinel, assuming Sentinal was used at the 10k mark). Make the 'reduced hate loss from taking physical damage' a native job trait (eg: 15% every 20 levels, plus 5% from Collar, 5%/10% from Creed feet +1/+2, 10%-20% from Burtgang).
One particular scenario that I've been in with two different groups is a setup of mnk (me) + pld + thf. One pld does a pretty good job with hate (though not ideal; I'd play it a bit differently, but I'm not asked to come pld since my mnk or thf is more useful), the other is... a bit slower.
In one particular fight, I had a really hard time with taking too much damage as mnk. To fix this, I had the thf collab me as frequently as possible, and TA the pld. It worked in helping to balance the hate between us, and things went reasonably well.
In a different fight with the less impressive pld we did the same thing. It didn't work. Part of the problem was not enough TA on the pld (this thf was also somewhat lacking), but I'm not sure that that in and of itself would have been sufficient. In the previous fight, the thf Collab'ing me turned the mob back towards the pld. In this fight, the thf Collab'ing me sent the mob chasing after the blm. Oops.
In each case, as mnk I was holding back severely, often getting to 250 TP and usually just using Shoulder Tackle as a weaponskill. I'd take occasional damage, but without Collab the mob never so much as blinked at the pld.
Not even going to bring up the third pld....
Different scenario, this time thf (me) + pld. No third DD aside from blm. In this case I always TA+WS the pld, and just do normal melee + SA otherwise (infrequent solo WS). In this setup, I -still- end up tanking a few minutes into the fight, often easily holding hate with just dagger swings (even using a gimpy Thief Knife offhand). In a couple fights I'd TA+WS the pld and then try to run around for SA and the mob would just continue to face me, this lasting for a full couple minutes (1-2 more TAs on the pld, no SA).
Essentially, the pld was a mostly useless accessory in the party. Gave tons of extra TP to the mob, making !! triggers more difficult, while not providing any particularly strong offensive benefits, and not being useful defensively (well, not entirely true; frequent use of Cover was also handy, once I got them to use it) without constant thf support. At best they're an extra cure, and maybe occasional Flash to help me evade an attack or two, plus a bit of a breather with Cover. But not a tank.
As seen in the DDs' DPS rates, there is just flat out no way that a pld can keep up with CE generated based on any of the tools pld has available. The only hope is to not lose CE as fast when taking damage in order to mostly stay ahead of the DDs (if the DDs take hate and get hit, they'll drop below the pld very quickly). Still need a good way to build CE quickly, though. Opening with a 900-1000 damage Vorpal (should be doable with good atma) while Sentinel is up would give ~2500 CE at the start, enough to be a workable lead.