A list of skills is a pretty good test, especially when you're comparing exactly what tools they have for DD. The simple thing I'm going to get across here is that DRG has more opportunities to do its crazy levels of damage.

WAR's WS loadout:
Heavy Swing -> Skull Sunder -> Steel Cyclone (WAR)
Brutal Swing (Side) -> Maim -> Godsbane
Path of the Storm (Back) -> Whirlwind
Overpower
Fracture
Mighty Strikes (WAR)

DRG's WS loadout:
True Thrust -> Heavy Thrust
True Thrust -> Leg Sweep -> Doom Spike
Vorpal Thrust (Back) -> Impulse Drive (Side) -> Chaos Thrust
Vorpal Thrust (Back) -> Ring of Talons (DRG)
Feint -> Disembowel (DRG)
Full Thrust
Jump
Dragonfire Dive (DRG)

What restricts DoW classes/jobs from going all out on DPS is a combination of TP generation and cooldowns. In general, the more time there is between your large damage WSes due to either them being on cooldown or you not having enough TP due to misses/waiting for swings, the lower your overall DPS. This is vastly more true on high damage mobs (Ifrit) and much less so on trash mobs/lower DEF bosses.

WAR's tools for damage are simple. Three attack trees: front, back, side, with 30s/60s/80s cooldowns on the combo enders respectively. Two of them end in AoEs, which is good times since SE makes us fight multiple mobs on more than one occasion. Then there's Overpower and Fracture, which are good in a TP-to-Damage-ratio but only occur when the WAR has hate, because they're being attacked. I suppose you could do something like keep a lesser mob alive and attacking you from the front in order to keep procing Fracture (40s cooldown) or Overpower (5s, much better) but in the latter situation, the lesser mob may die before long due to being hit that much! Berserk has been granted a buff lately, and I'm curious on how its actual numbers parse these days. I wish I knew- these days when I go WAR it's always as the main tank. Still, I pop Mighty Strikes whenever I go for a Godsbane combo, keeping me at full health.

DRG has, simply put, more tools for damage. It doesn't have a combo that starts from the side, only front and back. By comparison, however, it has four combo ending moves: Heavy Thrust, Doomspike, Chaos Thrust, and Ring of Talons on 20s/60s/80s/60s timers. Feint and Full Thrust proc on misses, something that can and will naturally happen on any content since 100% ACC is impossible- though since the removal of ACC penalties on DRG WSes, doing a multihit and counting on a miss to go immediately into Feint->Disembowel is no longer an option (a DRG in my LS was slightly saddened by this). Disembowel is technically another end to a combo, 30s, but of course it all has to begin with a miss. Jump is free damage/TP every 60s. Dragonfire Dive is okay. At least Power Surge's buff can be and has been numerically tracked-- something like +300 attack power? Definitely something worth keeping up.

However, DRG also has Keen Flurry, which helps reduce the problem of cooldowns restricting your DPS, as well as Invigorate, which reduces the problem of 'not enough TP.' And then there's Blood for Blood which gives free damage every 45s, 60s on a sub. I'm half-convinced that if you wanted to DD as WAR that you should go MRD instead just to get those three moves for Godsbane and Whirlwind.

Hilariously, MNK's loadout of WS cooldowns looks much like WARs, but I don't think anyone here is going to argue that MNK can easily be overtaken by a WAR.