I have both, well my Pigdog is Lynn Shell's hand shape and locally glassed iteration of the Super Pig Dog. But I think the Pig Dog was a specialty design for Outer Banks tube hounds (Jesse Hines first then Brett Barley), or at least has some origins with Lynn Shell, Jesse Hines and the original Super Collective of Shapers.
The short end of my interpretations and experiences is that the PigDog is more like a step up for getting into the wave and then holding a line in tube with confidence and kicking out or laying down a longer arc. But it is does not feel as shortboardy as my Ghost. The Ghost is very shortboardy if not completely and truly a shortboard for good shaped waist high and up. For my purposes I much prefer the Pyzel Ghost. I would say that I can paddle in a lineup with current and paddle into waves with a lot water moving better on the Pigdog. But the later drops and everything else I would prefer the way the Ghost handles.
The longer explanatory version is:
My Pigdog and Ghost are both 6'1. The Shell Shapes Pig Dog is 19.75 x 2.5 while the Pyzel Ghost is 19.5 x 2.65. The Pigdog has more volume due to the wider front half. Their foil is different though similar. Pigdog carries more foam forward through the nose with the little beakish nose (mine is very, very subtle), yet has a lower rail. I know Lynn Shell prefers lower rails on his designs. The Ghost carries more volume in the center and in the rail, but it is still a nice performance rail. The tails are very similar. The concave are also similar.
The Ghost is a shortboard for me. The Pigdog is a step up speciality board. The Outer Banks waves at size are slabby waves into the tube that often is either a closeout or a deep throaty one. It can be a full commitment and gamble kind of wave. You are often just kicking at the end or trying to find the door out. Thus the Pigdog's origins and intended purpose. Get it shorter if you want to have mobile in the tube and on the face. My 6'1 is more gunny for me at 5'10. The back half of the board is a gunnish design. Holds and is solid to stand on. But don't expect it to feel like a narrow nosed board.
The Pyzel Ghost is much more sensitive and "twitchy" than the Pigdog. Can turn in a tighter radius much more easily while it is still a very drivey design that carries speed into the turn and uniquely out of the turn. But I also would say the Ghost is one of my all time favorites. Lot's of front foot glide but then a solid yet loose back foot. It makes sense why it is such a good rocker for John John Florence. I like mine in waist to chest high punchy beach break but I would not even consider the Pigdog in that surf.