It really depends on the scene you're animating really. That's one of the best things about CH is that each workflow you described is equally as easy to do. Here are a few things to think about as you choose a workflow that best suites you:
1. Length - the length of the scene you are working on is a factor. If it is really long, then it's probably quicker to record both puppets at once and then trim away the visemes of whichever puppet does not happen to be speaking at the time.
2. Dialogue - If the dialogue you are working with is studio generated (you have control of each voice individually) and the length of the scene isn't too long to work with, then the best and cleanest way to get each puppet to lip synch is through the "compute lip synch from scene audio" function under the Timeline menu. If your dialogue is more naturalistic, like something you recorded organically of people speaking over each other/at the same time - then I personally prefer the previously described editing method of recording once and subtracting rather that editing additively.
Hope this helps! After animating a scene or two, you'll get a feel for what works best for you in any given scene.
Happy animating - AP
Took me a while to track down which video was the correct one, but here is a tutorial link from Okay Samurai on YouTube that I hope will help you...
Thank you so much, this is really helpful, regards, John