But if your "fall" was showing mercy, doesn't that mean that you're a paladin of devotion? (Ie it's not really a fall.)
For starters: no. You made an oath. You broke that oath. You don't just default to following a different oath.
Beyond that, they're pretty different.
The oath of devotion demands honesty, courage, compassion, honor and duty. You fall by not being 'good' enough. If your methods regularly include the use of deception you should fall. If you regularly choose to fight the bigger evil instead of defending the little guy, you should fall. If you regularly contravene the orders of those who have authority over you, you should fall.
The oath of vengeance requires you do what it takes to fight the biggest evil, show it no mercy, then clean up the mess you made afterwards.
There's a big gap between a vengeance paladin who grants evil creatures a chance at redemption and an oath of devotion paladin. I mean sure, technically you could fulfil the oath of the ancients, but thematically that's not a good fit either.
And right now: "I show mercy to evil creatures in the hope of redeeming them" breaks your oath, but is a mile away from consorting with demons and undead too. I mean sure, I could see a path from one to the other, but it's a long road and not going to be a fit for all comers.
In short: oath breaker is not a class for someone who breaks their oath and falls. It's a path for someone who falls and falls and keeps falling and voluntarily turns to evil in order to gain power.
Now maybe that's the logical conclusion of a paladin being unable to fulfil their oath, but it seems like a bad deal for the powers of light and goodness.