I suppose one advantage Pirate Bay had was that they set out doing something illegal, whereas Parler probably didn't even consider the possibility that they would have to fight to stay online.
Apple has tightened the rules around forums lately, I don't think they required moderation when Parler started.
The other thing is of course that Pirate Bay was started by hard core computer nerds, not business people.
TPB also has the advantage of age. Their last decade has been quite stable but back in the day they would regularly go down and people would make all sorts of witty comments questioning the competence of the operators. It took them a lot of work to get where they are and they also had/have a different scaling curve than a social network.
Don't forget the raid. On a hunch one of the admins was able to make a copy of the entire database and bring it back online shortly afterwards; if he had not, they'd've had to revive it with no content, and it probably would have died out / been overtaken by some other one.
Apple has tightened the rules around forums lately, I don't think they required moderation when Parler started.
The other thing is of course that Pirate Bay was started by hard core computer nerds, not business people.