I'm not an expert, but I've played enough Paladins to know a couple things. Here's a couple poorly formatted random thoughts about Defender and Champion

Defender: Most defensive by far. Pretty good for PvE. Even without taking virtues into consideration, they can solo the vast majority of mobs out there. It just takes a while because their offensive output is so low. You can (slowly) whittle down even the toughest mobs most of the time just by spamming some combination of angelswing and heal. For PvP, they took a massive hit when wrath changed to a 2-round sup. You won't get hit much in melee, but you won't hit very often either. Any non-shield-blockable damage will eat you up (which is literally everything but passive melee). You're still very much vulnerable to being bashed, especially from orcs (ie, savage feeding) and anyone with better passive melee than you (beefy APs, warriors using weapons you don't know). Giant could do ok, since shield bash is str-based, and they'd be able to reliably lag some folks. Ultimately, this is the survivable/PvE dedication though. You can land some kills with wrath spam still or just through luck or being super aggressive, but it isn't really a great option for aggressive PvP anymore.
Important skills:
Shield mastery: Beefy melee defense. Potential to block bash. Potential to block breath attacks. Helps you bypass shield block of enemies.
Shield jab: Think riposte with your shield (with potential to lag). Edges can pump it up to hit more often, hit everyone fighting you, and lag more often.
Angelswing: Two round skill. Blocks one round of combat from whoever you hit. Angelswing barehanded can silence for like 2 ticks. Angelswing with a mace can do some weak -str (not sure if it stacks). Angelswing with a sword doesn't do anything special.
Flank attack: 3 round skill that has to charge up. Blocks one round of combat, and a big hit at the end of the 3 rounds. You'll rarely use it after you have angelswing (unless you aren't tanking for some reason).

Champion: Champions are probably the most balanced dedication when it comes to offense/defense (Defender is defense focused, Avenger and Monk both lean offensive). They're pretty good at PvE as long as you're somewhat careful. They can use polearms, so you can slice which helps a ton against big mobs (they bleed while you rest, then go back to finish them off). Good for PvP also, since they lag better than any other paladins (avenger might be more reliable, but can't permalag). They don't have any real splash damage though, so once people know what to expect from you you'll spend a LOT of time watching people flee and quaff. Biggest weakness is losing weapon. Crunching kot, str-loss or even dirt/disarm is close to a death-sentence since you literally have zero defenses to fall back on. You'll absorb every hit coming your way if you lose your weapon, and there aren't very many no-disarm or even cursed staffs and polearms. It's also pretty hard to find very light weight weapons, so this will be your biggest struggle.
Important skills:
Bat: Bat is a minor damage (roughly half a normal swing) and is slightly less than one round lag (sometimes you can get 2 between combat rounds). Bat can lag. It isn't as OP as some older threads will lead you to believe, but it's still imminently useful in PK. You'll find yourself doing this a lot. It also gives you the possibility of automatic retaliation shots for attacks that aim for your hands (ie, disarm, kotegashi), which gives some (unreliable) protection from those attacks.
Fend: Fend is underrated. It's a feint against everyone who's fighting you, and has the potential to hit them back. It can also lag (lag seems more reliable when fending against groups, vs individuals). It also supposedly boosts your defense for a while afterwards, so it's worth doing at least once when fighting big mobs.
Marshal: Marshal gives you several options: Rally - Basically haste and + dam for you and your whole group for about 8 rounds or so. Phalanx - Super-defense. Makes doing things like tanking the Empire council pretty trivial. Forefront - Potentially rescue everyone in your groupmate from everyone they fight. Can also stop people from redirecting to them (rarely works, from what I've seen). Regroup - Group retreat. Has a cooldown of a few ticks.

Some general Paladin Tips:
- Use call lightning. Every time someone flees from you writhing/convulsing, your next action should be calling lightning. Not 'where' or an attempt to chase. Call lightning and try to catch them before they quaff. It won't always kill them, but a lot of times it will.
- Get empowered. I know priests don't require it anymore, but true Paladin goodness comes from virtues. You'll probably get them around lvl 25-30 and at (or close to) hero, as long as you're doing good things within your religion. They make a big difference and can dramatically change your tactics.
- Read the Paladin Code. Mechanically, Paladins have a lot of inherent power. Their biggest restrictions are RP-related. Do it the right way and your rewards will probably be better and you'll also probably have more fun.
- Fly. Lag is your biggest enemy. It doesn't matter how good your defense is, if you're permalagged by two clowns tripping you, you're going to die.
- Enlarge/reduce against bashers. Even if you're a giant, you can expect people to enlarge and try to bash you down.

Biggest threats:
- Shamans. Dispel and energy drain will destroy you really quick. Be cautious and ready to flee/quaff. You probably won't win this fight very often.
- Assassins. They can lag you about 15 different ways, which is very bad for you. They can also kotegashi, which destroys every Paladin except Monk.
- Thieves. They probably won't kill you, but they can annoy the crap out of you and there's nothing you can do about it since you can't reliably lag them.
- Neutral Outlanders. Paladins are built to fight evil. Non-evils that want to kill you can be a pain because they bypass a lot of your strengths.
- Orcs. Orcs are scary, because if they can bash you, you're dead. They can also wear you down quickly with bloodskins, or spinebreak until your protections fall.

Almost everyone else, you have at least an even shot at.