I'm not sure how much I like Smites being tied to spells (and no longer being Smite Evil)

I believe your tagline is in agreement with you.

Kind of miffed about paladins no longer being paragons of righteousness and justice

Oath of Devotion paladins are, at least. Though did you notice this sentence in the Alignment section: "Gold dragons, paladins, and most dwarves are lawful good." I thought that was curious, as the Oath of Vengeance paladin specifically contradicts that one. I wonder if paladins were more rigid at some point in the playtest, and that sentence never got revised.

I hadn't noticed that line from the alignment section, or at least I didn't notice the contradiction. Considering how many different iterations of the rules there were during the various playtest phases I'm not surprised some contradictions slipped in. And I realize the Oath of Devotion is the classic paladin. I'm glad it's supported on some manner. I like the other two Oaths, I'm just not super keen on calling them paladins. (Though the fact that all three Oaths are tasked with fighting evil helps.)

I suppose a lot of it was motivated by wanting to provide options in each class. Or they liked this Punisher-style character and didn't want to create a new class for it.

I have more trouble with the environmentally friendly paladin, that just seems like a strange fit. Plus, all that business in its oath about "The Light" reminds me of T'raltixx in Farscape's "Crackers Don't Matter". (So naturally now, if ever I play a paladin, I'll pick that one and spend battles shouting "I MUST HAVE MORE LIGHT!")

I believe the other two Oaths are meant to be versions of 4th Ed classes. The Oath of Vengeance is similar to the 4E Avenger class although I believe that one was a little more rogue/assassin-ish (Pathfinder has their own version of the concept called the Inquisitor) and the Nature Knight Guy has echoes of the 4E Warden (who was a nature-themed tank class).

Not sure Paladin is really the place to put them. I'd have loved to see a callback to some of the old 2nd Ed kits like the Wyrmslayer and Ghosthunter instead. (Or even something like Pathfinder's Warrior of the Holy Light, where you give up spellcasting in favor of various auras and light-based powers.)

Oh, right, the Warden. I'd picked up on the similarity to the Avenger's raison d'être, but missed the other one's antecedent.

The only real commonality - and it's not what I'd deem central to the other two - is the whole oath business. And finally I've come up with a paladin concept I'm interested in, as I now intend to create a gold dragonborn paladin/sorcerer specializing in air magic, called "Oath Windenfyre".

::golf claps::

Alas, it will take more effort to convert to 5e my dual bastard sword-wielding wood elf, Julien Fryze.

Actually, the latter shouldn't be too tough other than having to wait until 4th level when you get your first feat (which is my one knock on the game. I like that all the feats are significant, but it's annoying that some concepts have to wait until 4th level, unless they're human.) and taking Dual Wielder. Longswords are bastard swords now (which is more historically accurate, as the terms were basically interchangeable). The weapon D&D previously called a longsword had a bunch of different names, but was commonly just referred to as a sword.

Actually, the latter shouldn't be too tough other than having to wait until 4th level when you get your first feat (which is my one knock on the game.

It's all quite doable, but the primary issues are:

1. Wood elves are no longer ridiculous cheese weasels. Have to choose a different race.

2. As you noted, no more bastard swords (he would have to stat them as longswords, of course). That is key to the character (he calls the right one "Magnificent" and the left one "Sexy").

I think of a bastard sword as being a longer sword than the longsword, one that you have to take a feat in order to wield one-handed.