JadeVib

Tenets: Both encourage you to put yourself in high danger, but Vengeance also encourages you to be merciless. That can cause social challenges. Edge Glory.

Oath Spells (LVL 1): Hunter's mark is a big benefit and not otherwise available to paladins. Bane is Heroism, which you could choose to prepare anyways) is nearly useless once you hit 10th level, and only conditionally useful before then. I'd rather spend my concentration on something else. Guiding Bolt would be good if not for the ability to do more damage with a smite (2d6+2d8+strength/dex vs 4d6 with a lower attack bonus). Still, at greater ranges or when an ally really needs advantage, It has a place. Still, large edge to Vengeance.

Oath Spells (LVL 2): You get these at 5th level. Enhance ability when you already have an option for advantage on Athletics and Acrobatics is a bit of a waste. Magic Weapon is a situational want, and you can already prepare it. Hold Person is a nice emergency stop, even with the lower DC, and Misty Step is huge. Large edge to Vengeance.

Oath Spells (LVL 3): Identical. Strong options at level 9.

Oath Spells (LVL 4): While both lists are fine, the Dimension Door is the winner option here that will be used most often. At 13th level, it holds up as a useful spell for retreat or closing with a distant ranged enemy. Large edge to Vengeance.

Oath Spells (LVL 5): 17th level is rarely reached, and both provide some conditional benefits. I'd call them a wash.

Channel Divinity: Peerless Athlete is a nice to have option, but far from a significant benefit. You also have a bonus spell that does much of the same work. Inspiring Smite is the better option, and gives you a way to heal as a bonus action allowing you to fix multiple PCs - but until you reach higher levels, it requires your channel divinity, bonus action and a spell slot for the Smite. And, you need to hit to do it. Abjure Enemy, even when the save is made, is a huge benefit to the party in that it locks a big threat down with low mobility. Vow of Enmity is also super strong in combat in games where advantage is less common and the enemy has a high AC. Large edge to Vengeance..

7th level Abilities: Both grant some mobility, but the Oath of Glory is much better. Extra 10' movement over a very conditional +15 already favors the paladin, but the ability to give that extra movement to allies, especially at the start of combat, is huge. Edge Glory.

15th Level Abilities: An extra 3 or 4 attacks and avoiding 3 or 4 hits can be huge for Glory, but the timing of them is hard to control. However, being able to make an extra attack whenever your Enmity Foe attacks you is also huge, but requires you to draw in those enemy attacks. I call these a near wash, but edge to Glory.

20th Level abilities: 20th level abilities are not that important due to lack of use opportunity. Living Legends is fine, but you should not be missing a lot at this level, Rerolling failed saves when you have the highest saves around, as does your party from your aura, is less useful than you might think, but can be a day saver. The ability to reuse the ability with your 5th level slot sounds nice, but you may want that for a smite or a spell. However, it is a bonus action. The Avenging Angel gives you huge mobility with flight, and a saving throw or frightened for every enemy within 30 feet of you (once each per combat) can also be a huge benefit. However, it requires an action and that means you need to be prepared for combat or you're giving up a round of attacks. The abilities are mostly irrelevant, but I give Glory the edge.

Overall: They're both certainly playable and you should pick the one that matches your character concept. However, if you're playing a low level game, I'd call Vengeance clearly better up to 7th level. Then they begin to balance out, but for power gaming I would still stick with Vengeance. At the highest levels I think they remain close to a wash with Vengeance still being a bit better.

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