I'm in a Werewolf campaign at the moment so I'm familiar with this. Some pros and cons:

Pros:

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- More narrative 'realism': For those who have... issues with the abstract nature of HP (*side-eyes other HP thread*), health levels are more cleanly mappable to states of injury or seriousness of attacks.

- More 'grit': There generally tend to be far fewer health levels than HP (by necessity, nobody wants 20 or more of these things) and you don't usually get more of them as you level. This keeps even relatively mundane combat dangerous. Werewolf includes a soaking mechanic to help you deal with most muggle opponents, but all it takes is a bit of silver or other source of aggravated damage to keep the difficulty up. Depending on the type of campaign you want to run this may be more of a con, since getting taken down by a lucky mook never feels particularly heroic.

- Easy injuries: You don't have to do any math to figure out injuries or effects tied to HP thresholds, because your health IS the thresholds. Other things like crits are also easy to figure out, e.g. a crit deals 2 levels instead of 1, no need to fiddle with multipliers or threat ranges etc.


Cons:

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- Swingy combat: As mentioned, fewer measurements means much less room for error. A few (un)lucky hits and you'll be needing a new character sheet.

- Combat spirals: These systems tend to tie negative effects to each lower threshold that then stack or scale. This can make comebacks or recoveries very hard to pull off, which feels particularly bad if you got put in that situation/incurred the first few negatives due to bad luck or misunderstanding rather than skill.

- Limits campaign/combat types: The nice thing about HP is that it's so flexible - you can make a game, a session, or even a specific encounter more gritty or heroic just by tweaking the damage from each hit relative to the party's HP, and then change it dynamically on the fly. Your party can take on an army of mooks that barely scratch them one minute for more of a heroic feel, and then be forced to flee for their lives from a rampaging dragon the next, followed by creeping through a scary crypt with their healing deplre, all by adjusting how much damage per round they'll take if they don't otherwise act.

- Lack of Divisibility: the abstract nature of HP means you can marry or divorce them from all kinds of rider effects without having to redesign your thresholds. Want someone who is healthy but poisoned or fatigued? Wounded but enraged and focused by adrenaline, then gets wounded some more? HP is flexible enough that you can layer on as many of those states as you want, or simply go with the default of "1 HP left means no loss in effectiveness" if you want.

- Nonstandard health states: Because you have to define each threshold and what happens there, it limits your design space to go outside that framework. Things like temp HP/buffers, bleeding (including bleeding out) require additional design and tracking. Instead of "you lose 5hp per round" for instance, you might have "if you bleed for 3 rounds you go down a threshold" which is a bit easier to lose track of.

- Mappability to other games: This is perhaps the #1 reason to use HP; they've been around in RPGs for years, including video games. This is especially true if you have players who are newer to tabletop, by using HP you're using something they're likely familiar with from elsewhere and that's one less thing they have to keep track of.


Given that I have more cons my own conclusion (that I prefer HP) should be apparent but health thresholds aren't bad, they work well in several systems.