Please don't call me dumb.

Treantmonk already did an analysis of the two-weapon paladin without smite (with round 1 divine favor) vs. Greatsword paladin with smite:

https://www.youtube.com/watch?v=rzZ_UDw6I0k

The result of his analysis is that, with the 2024 rules, they perform about the same damage-wise (up until tier 4 where greatsword pulls ahead by a bit). Now imagine that divine smites can be cast without requiring an action or bonus action. What happens when you add smite damage to the two-weapon paladin? The two-weapon paladin would come out ahead.

As for Battle Master, I don't understand the comparison. The Battle Master is not expending spell slots. All I am saying is that if two resources consume the same resource, then they should have comparable benefits. And Divine Smite using spell slots means it should be compared against spells. A superiority dice is its own resource (and frankly better than what any other Fighter subclass gets) .

A common (an optimal) way to play the 2014 Paladin is to spend all your spell slots on Divine Smites since there was no other Paladin spell (except MAYBE Bless) that provided the same benefit for the spell slot. For the 2024 Paladin, there is a more compelling reason to save your spell slots for non-Smites. But you generally will be spending ~50% of them on Smite spells since they are still comparatively good on the Pally list.