I think a lot of it comes down to the failure of the expected encounters per day paradigm that 5e was designed around. The simple reality, I've found, is that in most games this paradigm just doesn't play out, which significantly benefits classes that can blow all their resources quickly with an expectation of getting them back before the next big fight. Short of being in an active dungeon with constant threats, there's no real way to enforce the paradigm that doesn't come off as contrived.
This benefits paladins immensely since it means paladin players can essentially feel free to burn slots on smites.
This is the primary factor right here, I agree.
If you only have 1 to 3 encounters in the day before you take a long rest, the paladin's spell slot table becomes almost "short rest based". A Battlemaster Fighter should theoretically be getting more overall Superiority Dice over the course of a day than a Paladin does with their spell slots... if the number of combats *and* short rests are part of the expected allowance of 6-8.
However, I think we've seen by thread after thread after thread that that allowance does not happen that often, especially to many tables. The way some people are speaking, it seems as though throwing a Vow of Enmity and then mega-critting is the norm and expected operating procedure for their table's paladin. Which kind of implies that a single big combat once per day is their norm (since VoE is a long rest resource.) Which, taken under that lens, absolutely makes the paladin very powerful at those tables. If you primarily only have one fight a day (which can imply a "large" battle with probably at least one very "powerful" enemy), and the table's Vengeance Paladin is throwing up a Hunter's Mark, Vow of Enmity, and then smiting over and over against that big enemy... then sure they are doing to do massive damage each and every battle (because everything refreshes after each one.)
But someone above pointed out the Paladin being weaker versus multiple enemies... which I take to mean both "multiple enemies" during a single fight, and "multiple enemies" over the course of an entire adventuring day. If your table actually does manage to have 5, 6, 7 combats in the day... and those combats involve 5, 8, 12 enemies at a time... the Vengeance Paladin ends up having to lose more slots Hunter's Marking more often, has to pick and choose which fight and which enemy to use VoE on, and ends up with so many targets that blowing through all of the spell slots smiting and then having none left over for the rest of the various fights becomes a real possibility. And once that happens... once the Paladin has "blown" all their stuff... the rest of the day for them can be painful. Which is why in the few times I've seen a Vengeance Paladin in play *at* a table that has more fights and more short rests, the player ended up being much more judicious with their spell slots and
did not choose to nova all the time.
At the end of the day... like everything else in the game, how something plays to make it seem "overpowered" or "underpowered" is going to be contingent on the style of play at an individual table. And yes, at the tables that usually do one large battle each day and then are able to long rest... the classes built on long rest mechanics will seem much more powerful than the ones who operate on short rests. But of course, the opposite is true for the opposite tables. After all... I have a Battlemaster player with the Martial Adept feat who now has like seven Superiority Dice per short rest that is throwing out extra damage *and* parries *and* riposting *and* tripping enemies giving everybody else Advantage *and* Commander Striking the rogue to take advantage of that... *and* of course having their own short-rest based "nova" via Action Surge. So while the BM F doesn't have that "Wow!" effect like a paladin would in a single fight... they are doing a lot more varied stuff and helping out their teammates over many more encounters.
Which is pretty much the way the classes were meant to be built after all.
