Burst vs. Sustained DPS
There are several reasons why burst is important. It concentrates a greater proportion of your dps into relatively fewer GCDs. This means that:
1) A greater proportion of your dps falls under raid buffs.
2) You can time your burst such that a greater proportion of your dps occurs during high uptime sections of the fight. This means that you are generally punished less for time off of the boss.
3) Your dps relative to non-burst jobs increases in fights with a lot of downtime (i.e. no targetable mobs present, boss using their special move animation). While you're all sitting around waiting, the time to your next burst phase is ticking down. You spend a greater amount of your active time in burst.
4) A number of mechanics require you to burst down an add in a fixed amount of time.

Common sense would dictate that, if you have two jobs in the same role with different amounts of burst, the job with the higher burst ought to do lower dps under target dummy conditions. This way, the burst dps job pulls ahead under lower uptime conditions, and the sustained dps job pulls ahead under higher uptime conditions. It's a bit like being forced to trade off acceleration/handling for a higher top speed in a racing game.

Unfortunately, this isn't the case. So while you can have two jobs on paper which could do similar dps on a target dummy, the one pulls ahead under practical conditions including unfamiliar mechanics and human error. You end up needing to play perfectly and needing to work much harder to narrow, but not entirely close the gap.

DRK and Burst
On first glance, you might think that DRK can burst whenever they want to. In a very limited sense, this is true. You can pool up your resources and then use them all at once.

But Dark Arts is not multiplicative. It's additive. You gain 140 potency for using it irrespective of how powerful the GCD is. Use it on Syphon, and it's a potency increase of about 1.63x. Use it on Souleater, and it works out to be about 1.46x. Use it on Bloodspiller and it works out to be about 1.35x. It doesn't make your big hits proportionally stronger (out of necessity, of course, because then you would be using it preferentially on Souleater/Bloodspiller). You're better off thinking of it as a 140 potency oGCD than a damage boost.

DRK does not "burst" by pushing out more potency into a smaller set of GCDs. It "bursts" by pushing out a fixed potency boost for longer. Blood Weapon and Delirium just give you resources to sustain this.

This is one of the places where DRK fell behind between Heavensward and Stormblood. Req and IR both represent an additional layer of burst to their respective jobs. Delirium is relatively underwhelming because it has an expensive resource cost attached, and extends Blood Weapon rather than making the window more powerful. You can contrast this with IR after the rework, where a shorter, more powerful window widened the gap between tank dps.

I think that Delirium, as it stands, needs to be reviewed so that it offers something of proportionate value.

DRK and Raid Buffs
This should come as no surprise, but in a game where burst is so important, DRK is required to play around the timing of raid buffs. You need to push out as many DA usages and Bloodspiller usages as possible under infusions and raid buffs. The only difference is that you're doing it without the aid of your own damage multiplying buff.

It also doesn't help that the 40/80s timing of our resource buffs is somewhat out-of-phase with the traditional 60/120s timing of many other raid buffs.

I don't think that "burst" has to always equate to a simple damage up buff. Wildfire is another example of how a buff can concentrate a lot of damage into a relatively short span of time. We've already talked about how, under the present system, players want to fit in as much DA usage as possible. Ideally, Delirium should reflect this, either by making individual uses of DA more powerful, or by delivering a burst of damage at the end of the window based on how much DA you use.

With the way raid buffs are designed, I think it's too much to expect DRK to keep pace without a greater degree of burst. The solution to this lies in making Delirium into a more impactful burst cooldown, and possibly making Bloodspiller come up more often.