[Toa Circuit]

It would be akin to the continuous methods, though a little bit faster, I would suspect.
You're likely to have an unfun time splitting out something like a PID controller to a separate thread- and for no benefit. In my experience, PID doesn't take any resources- or not enough to cause lag. I've ran a few PID loops (Of my own making- not the builtin class.) concurrently through the TeleopPeriodic functions, with no problems... what PID algorithms are you using that take lots of resources?