And just to make things more complicated, I'll give the other side of this opinion. I have a Greenback in house for 2 years, in an identical cab to my Private Jack. I played both with Classic 30, Egnater Rebel 20 and Tweaker 15, hand made AX84 High Octane, Mesa TA15, and Mini Rec and Budda Superdrive 18. I preferred the PJ with every one of them, over the greenback. Sold the greenback, and have since played the Private Jack with my Mark V25 and PRS 2 Channel H.
Any amp that I want Greenback tone with, the PJ delivers!
I prefer the Eminence Legend GB12 over the Private Jack. The GB was Emi's first 'British cone' speaker, and I always thought that the Private Jack would be virtually the same speaker...but that is not the case. The Private Jack doesn't do anything for me. I hear it as a flat, dull speaker...whereas the Legend GB12 Eminence has a big firm low end, a warm woody tone, and smooth high end when pushed. These two speakers have the same voice coil diameter and the same size speaker...but those are the only similarities, ime. The Private Jack is more expensive, too.....but it wouldn't matter if it were half the price of the GB12...I would use the GB12.
I think the private jack is a fine speaker...not my favorite, but good. I actually have it in my rectoverb combo at the moment and like the sound. It helps take away the modern, kind of sterile sound that the boogie has.
I'm not an expert at describing differences in speaker tones, and I'm comparing it to the stock Blue Marvel that came in the C30, but it smoothed out the highs just a tad and sounded more 3D if that helps at all. It sounded especially good with a Wampler Super Plextortion. Unfortunately, I'm guilty of letting both the amp, and that now discontinued pedal go in my quest for something "even better". I've finally landed on a DSL40C with the creamback, but I still sometimes miss that C30.
I bought 2 to go with a 30 watt version of the 5e3 I was hand building. My thought was this thing would replace my Twin. It could but I made the cab so large it's too much a pain to haul around but that's another story. I thought the Private Jacks would be a little more mid rangy than the typical Amercan voiced speaker. I mounted them vertically. The speaker is brighter than a green back and has a tighter sound. I make this comparison because I've heard people describe them as higher powered Green Backs but I would disagree. I also discovered I prefer one speaker to two and I like it off the ground. I think it delivers great clarity while staying full sounding. It also has a good power handling capacity and gets pretty loud. So I'm a fan.
I also use one with a Mesa Boogie Express 5:25 which I like to run in class A mode.