Yeah. I think if you’re comparing apples to apples (IIC+ mode on the V to the dirt channels of the JP-2C) then the amount of compression is about the same. Channel two is a little less compressed than channel three. This is ignoring all the other differences Bandit mentioned.
I think all of these are pretty low in compression for such high gain circuits, certainly compared to Mark IV mode. But I’m coming from an EVH 5153 and a Cornford MK50, both of which I found very compressed. My old Soldanos and Bogners seemed more compressed at high gain too; but everybody hears things differently.
It’s worth pointing out that something like compression is not easy to compare sensibly, as everything has different compression characteristics; for example the Cornford cleans up beautifully and has great exciting high mids - which makes it feel uncompressed in the room, but when I recorded it, I noticed the level meters were very flat and it didn’t jump out of the speaker - which made it difficult to mix sometimes. The EVH 5150 III felt pretty darn compressed and almost antiseptic in the room, but it had a “tear your face off” quality that translates really well in a mix. The Bogner feels very, very organic and lovely under the fingers but the high mids just squish so hard it’s almost impossible to record it next to a Marshall-type amp and get convincing results.
I think, on balance, any IIC+ circuit is going to be relatively uncompressed, touch responsive and easy to mix relative to other options (it’s certainly my favourite) but others hear all the saturation and thick midrange and go “ooh it’s so gooey and compressed”. In short there’s no accounting for taste.
I think that (in a nutshell) if you like IIC+ mode on the V, you will love the JP’s channel three, and I think you’ll find its channel two clearer, crunchier and less compressed than either - discounting all other differences.