Oath of Vengeance vs Oath of Heroism Vs. Splashing Champion as well

[Citadel97501]

Hello all, I was just wondering which is better for crit fishing? I am pretty sure Oath of Heroism (Unearthed Arcana) is slightly better as its harder to get the 19-20 critical hit benefit vs. the simple advantage available for the Vow of Emnity? However, a few things come up which I think will skew this quite a bit. I am working on a half-elf character build to focus on crit fishing with the Bard: College of Swords, and I am pretty sure the Elven Accuracy will skew this back in favor of Vow of Emnity due to dependability?

Without Elven Accuracy
Vow of Emnity 3: 9% chance of a critical hit, but is considerably more accurate due to innate advantage.
Oath of Heroism 3: 10% chance of a critical hit, increases to 19% on if you can get advantage another way.
-19% chance with Advantage...

With Elven Accuracy
Vow of Emnity 3: 12% chance of a critical hit, but is considerably more accurate due to innate advantage.
Oath of Heroism 3: 10% chance of a critical hit, increases spectacularly depending to 27% if you can get advantage another way.

Other Options:
Another option is splashing 3 more bard levels into Fighter but this seems overly expensive as then you won't have your infinite blade flourishes at a d6 till level 20, and will lose 9th level spells at the end of the build.

[Evaar]

You could go pure Heroism, use Find Steed, pick up Mounted Combatant, and dual wield scimitars. That would make your standard turn (with Channel Divinity against Medium or smaller enemies) three attacks with triple advantage and 19-20 crit range.

Separate from that, I think if crit fishing is your goal then Heroism is your oath. There are many ways to get advantage from your team; just ask them to help you with that. Not only that, but Heroism has more synergies from crits.

[Khrysaes]

I am not sure a 3 paladin/ 3 champion would stack their effects to increase critical hit beyond 19-20. Champion is likely a waste.

Greater find steed can be your bard magical secrets at 10.

2 or 3 hexblade would be better than champion as well as you can get reliable advantage from devil's sight and darkness or an invisible imp.

And hex curse to supplement the channel divinity.

[Benny89]

For pure crit fish I would go Dex Heroism Half-Elf and multiclass to any warlock after level 6 or multiclass to Lore Bard. Or Classic go CHA and pick Hexblade.

Take Half-Elf Drow so you can have at least Fearie Fire till you get to appropriate levels and rely till then on your team to get advantage.

After level 6 multi to either:

1. Warlock - I would grab Archfey for Fearie Fire so you can use that since first level dip, Hexblade if you go for SAD CHA. Fiend is also nice with his THP getting back on kills (which loads your Armor of Agathys is you use one). Anyway our main goal is: Fearie Fire/Darkness with Devil's Sight and then Shadow Of Moil. FF is nice because if enemies have blindsight/tremoresight - SoM is useless, but you then have Fearie Fire.

2. Lore Bard - Fearie Fire and more slots to smite from. At level 6 Magic Secrets - grab Shadow Of Moil.

Mounted Combatant is nice but till greater steed your mounts are squishy and die super fast, also barding costs gold + you need to spend feat on this one.

Imo multiclassing is better option for getting advantage.