I thought it would go without saying that they can only be identical sounding as far as the amp and cab modeling goes. I didn't think anyone expected the pack to f.ex. make them a cleaner, faster and better player. Now that's a pack I definitely need to buy! 
Seriously though these seem to work really well with just about all humbucker guitars as many of the demos that I put out were actually tracked on a PRS and not my Music Man. I would say that if the pack does fall short for you then one likely reason is how you play the guitar.
There is truth to geurtsema 's point because the way JP plays is to have a tight low-ish gain amp settings and pick pretty forcefully and mute a lot of the strings with both hands all the time. If you don't know this technique then you're most likely not going to have that forceful rhythm sound. Here's an example from the studio of JP tracking the second verse of Forsaken: https://youtu.be/V3YWDg1sY1I?t=285
Notice how he picks all those chords so hard that his whole body is moving and at the same time his left hand mutes the strings to dead silence. This is how you need to play if you want to have that aggressive attitude that JP has in many of his riffs. If you have a much lighter touch then nothing can make you sound like that. That hasn't been the case luckily but it's really hard for me to tell someone that their technique is the reason they're not "getting there". 
I wasn't really impressed with the JP2C. I actually much prefer my Mark V. That being said I have a real Mark IIC+ from 1984 - that's the one I'll be making. Here's a video of me playing around with it: https://www.youtube.com/watch?v=h9DAPK87gnQ