Is the Oathbreaker paladin's Channel Divinity option Control Undead based off of character level or paladin level?

Question

The Oathbreaker paladin's Channel Divinity feature states (emphasis mine):

Control Undead. As an action, the paladin targets one undead creature he or she can see within 30 feet of him or her. The target must make a Wisdom saving throw. On a failed save, the target must obey the paladin’s commands for the next 24 hours, or until the paladin uses this Channel Divinity option again. An undead whose challenge rating is equal to or greater than the paladin’s level is immune to this effect.

Is this ability based on character level or paladin level?

Answer 1

It's paladin levels

For these reasons:

1. The rules are written assuming only single class characters except when explicitly dealing with multiclassing.

2. There are vanishingly few features that use character level rather than class level. Off the cuff, Cantrip scaling and proficiency bonus are the only ones I can think of. It is explicit that they use character level.

Answer 2

When something uses your total level, it says so

The rules on Multiclassing include the following:

The experience point cost to gain a level is always based on your total character level, as shown in the Character Advancement table, not your level in a particular class. [...]

Your proficiency bonus is always based on your total character level, not your level in a particular class. [...]

A piece of the PHB errata to this section states:

If a cantrip of yours increases in power at higher levels, the increase is based on your character level, not your level in a particular class.

All of these cases explicitly use your total level and not your levels in a class. Lacking a similar exception for the Control Undead feature, we conclude that it uses your class level and not your total level.

Furthermore, multiclassing is an optional rule so it makes sense that the rules weren't written to account for characters with multiple classes. This would explain why proficiency bonus, cantrip scaling, and experience points needed to be called out explicitly and why Control Undead would be about your paladin level.