It’s just a crunch setting of the same basic circuit. Probably does have a slightly different EQ curve to it. I just wouldn’t consider it a different “mode” like on the V or VII. It’s like the III having the R2 for a rock rhythm channel but with more gain available.
When I first played a JP-2C I was kind of underwhelmed with it at the time but I got to play one today after it having been some time and gotta say it sounded pretty good to me. I didn’t care for a VII I tried when they came out, so maybe I’ll like that in 2 years as well.
With the feature set the JP has, the reissue would have to sound markedly better to not get a used JP instead.