NOTE: This poll is marked 5E because I use specific mechanics from that edition to set up the scenario. Obviously it could be adjusted to fit other versions of the game.
Here is the situation:
The party is in a fight for their lives. They are in combat with a powerful, intelligent enemy who has a powerful (save based) attack that does a significant amount of damage. Even on a successful save, it is enough to drop any one of the wounded, near spent characters.
The party has a Fighter who is up in the BBEG's grill, getting ready to hit him hard. Based on previous rounds, it may be hard enough to drop the BBEG.
The party has a wizard who the BBEG has seen cast a lot of spells but not his top tier spell.
The party has a rogue who is sniping from behind cover, and a successful hit is more or less just as likely as the fighter's hit to take the BBEG down.
The party has a cleric who the BBEG knows has spent all of their big magic and could potentially yo-yo a fallen character but not do any significant healing.
The BBEG, as stated, has an attack that can almost certainly drop one of those PCs, as well as bonus action that the BBEG can use for Misty Step or similarly "safe" movement. It is the BBEG's initiative and no PCs have held actions or reaction abilities beyond a standard OA.
You are the GM. Who does the BBEG attack? Why? What then?
I mean if he can be taken out by
either the Fighter or the Rogue in a single round, it's 100% all over the BBEG.
He has lost.
There is no chance of him winning.
Check and mate.
Whoever he takes out, the other PCs will almost certainly kill him the next round, especially as with a "man down", they will blow absolutely anything to take him out. Even if he could repeat the "death attack" next round, he's still going down with great certainty.
So really have to consider his psychology and escape options. If he's sane and wants to live has some way to escape, then forgoing his "nuke a man" Action and bolting for the escape with a Dash, especially if he can use the Misty Step-type deal to get even further away (or maybe through something the PCs can't immediately/easily follow through) is the right thing to do.
The Fighter is a bad idea if they're 9th level or more as they will have have Indomitable and assuming that's not blown, could re-roll the Save. The Rogue is going to have the best chance to chase him, because of stuff like Bonus Action Dash.
If he's not sane or doesn't want to live or would find it dishonourable to flee (i.e. he's an idiot or fanatic, try getting a wedge between those two), just to cause the most harm possible, I think go for the Cleric and ideally find a way to not just drop them, but kill them outright, so that a Revivify would be needed, which the party probably not cannot easily access. So you'd be creating a really annoying situation. Also, if he's willing to ride the dice, and accept the tiny, tiny chance (probably like 5% or less) that he won't get killed the next round or the one after, due to lucky rolls, the Cleric remains the best target, because it will panic the party somewhat, and none of those classes have easy access to a way to get the Cleric back up. So, it probably wouldn't work, but you drop the Cleric, get lucky with the Fighter and Rogue's attacks, and the Wizard's spell, drop the Rogue. Now you have a choice again - do you flee, with the only character good at chasing down, and their healer down? Or ride the dice further, and hope to take out the Fighter or Wizard? Probably the Wizard. At this point, the Fighter almost certainly is going to kill you unless he has the worst dice luck in history, but he'll have a very annoying pyrrhic victory to deal with, and three people to try and stabilize (assuming you didn't manage to kill-kill them) and/or cart back to civilization.
But again assuming he's sane and wants to live, and has a way to escape, not messing around trying to kill people is his best option - if the Rogue catches up to him, maybe spend a round dropping him, but not otherwise. Just run for the hills, escape zeppelin, big chute into the underdark, comedy cannon, or whatever.