Out of these two, the plea bargaining system always seemed the most corrupt to me. It's also widespread (in some form^) and predates privatization.

I say some form, because confessions forced with threats of far worse punishment are a long unbroken tradition. It used to be more common for them to happen after sentencing, say during your punishment.

The modern form usually revolves around an enormous range of potential punishments. 6 months probation if you confess/bargain, 6 ears in jail otherwise. It's especially malicious because it's all happening between lawyers, without judicial involvement. Well paid lawyers are important in courts too, but at least there is a neutral judge in the room.

It's not unique to the US.