FrogReaver
The most respectful and polite poster ever
For simplicity's sake, I'll just model the Paladin's hit rate at 60%, and the spellcaster's DC results in an enemy failing the save 60% of the time ...
Fireball (3rd-level slot):
.6*28 + .4*14 = 22.4
Single Divine Smite (3rd-level slot)
(Paladin level is 9, has longsword w/ Dueling FS and 18 STR):
(1-(1-.6)^2) * 18) + (2 * .6 * (4.5+6)) = 27.72
So in this very simple scenario, the single Divine Smite turn is outdamaging the Fireball vs. single target by about 24%.
(Of course, the Paladin also keeps his spell slot if he misses both attacks, but I don't know how to model that part mathemetically.)
A caster will have 5th level slot by the time the paladin has 3rd level slots.