It makes sense if we're comparing War's (vit) vs. War's (str). As you said, a War putting out half the effort of a perfect War can outdo the better player simply by putting on Str accessories. In that regard, they type of gear makes a huge difference. You're also right that when you're comparing War's in Dps gear to actual Dps in Dps gear the dynamic changes, but that is precisely why I pointed out the two factors that stack things in War's favour.
Simply put, to maximize their Dps, War's have to rotate two combos, one DoT, and use a single OGCD. That's a mere 8 move rotation in which the OGCD takes care of itself and does not interrupt combos. On top of that War's typically get 100% uptime on the boss. By comparison, a Drg has 2 complete combos, 2 4th tier finishers that are interrupted by other moves and must be used as soon as possible, one Dot that can interrupt combos, one buff that can interrupt combos, 5 OGCD's that are most often used on CD (except for Geirskogul, which is more complicated at a burn of 1 ever ~90 seconds), and all of these things must be used while keeping a close eye on that BoTD timer to make sure you don't mess it up. That's a 15 move rotation that is constantly being interrupted by boss mechanics, because Dps rarely get 100% uptime on Raid bosses.
Normally, Drg's are complete powerhouses on single target Dps. Evenly matching gear (slaying for slaying) with a War, the comparison should be dramatically in favour of the Drg. However, a War can, and often does, keep up, because those two factors (simple Dps combo and 100% uptime) make a huge difference to the end result. Personally, I think this is a huge mistake on SE's part, and reflects how utterly silly the current end-game meta. SE is responsible for fueling the idea that War's in Vit gear are "crappy wars" by creating a system that allows them to meet Dps standards.