I think this is actually a fire-water-grass thing.

So Dalinar's army stands basically no chance against TLR + inquisitors + nobles + kandra + koloss + nobles' armies. They're a conventional army that uses metal, and TLR alone could basically wipe their entire main force. But even if TLR doesn't participate, then Koloss alone with Inquisitors to emotional push them towards places decimate the main force if it is separated from Shardbearers. TLR is needed to kill people like Jasnah, Kaladin, and Szeth but he can still do so with ease.

On the other hand, they actually do pretty well against Vasher and his army of Lifeless. They're basically similar to thunderclasts in function, and obviously Shardblades are made for this sort of thing, plus a conventional army with a bunch of big hammers actually has a decent shot at fighting these things with proper leadership unlike the several tens of thousands of koloss. Both sides have Nightblood here and while Vasher could use it to obliterate the army I still think that even in this scenario what is left of Dalinar's army can win. Vasher's weakness compared to TLR is that there is not a lot he can actually do against someone like Jasnah if he isn't hyper aware.

Lastly, I think Vasher's army has a solid chance vs TLR. Armies in Scadrial are a bit of a formality and I doubt they and the Koloss would actually beat the Lifeless army. Also, unlike particularly powerful Shardbearers, I think almost all Mistborn can be fairly easily dispatched by Vasher. The Allomancers probably can't do anything against the Lifeless either barring a very hard, blunt object and a lot of pewter. TLR is broken and would probably instantly wipe the battlefield, so Vasher's army would probably still lose, but there's one reason he has a chance. TLR is supremely arrogant and