I almost feel like this needs two separate topics in a way, because Tex Slazenger and Shanghai Pierce in WCW were so different from The Godwinns in the WWF (and later Southern Justice, but they weren't really around long enough in that role).
I realize this team pre-dates their debut in WCW, but I'm going to start with their time there because that's where I first saw them.
Nostalgia may be fueling my opinions, but I remember Tex Slazenger and Shanghai Pierce being a really fun midcard heel team during the era of WCW Saturday Night. Particularly memorable, for me, was their "crazy" (at the time) match against The Vegas Connection - DDP and Vinnie Vegas (Kevin Nash).
Shanghai Pierce was masked at first, then lost the mask in an angle, but I can't recall the particulars. I always found it strange that one of the members of the team had a mask and the other didn't, but it was cool too. As a kid, Tex Slazenger seemed like the "leader" of the team to me. This is a point I'm bringing up for a reason and will come back to again in a minute. For whatever reason, Tex and Shanghai never won gold in WCW despite being one of the more "over" teams on the roster.
I wasn't nearly as enamored with The Godwinns in the WWF, even though they were the same wrestlers. Chalk it up to the gimmick, I guess. Of course, Henry O. Godwinn (Shanghai Pierce) was a WWF singles wrestler at first. His most (in)famous feud was with Triple H in a "Hog Pen Match" at one of the In Your House PPVs. At some point, Tex Slazenger appeared as a jobber for at least one match on Superstars or one of those shows (maybe under his real name Dennis Knight, but I can't remember). Eventually, Tex debuted as the dim-witted Phineas I. Godwinn and reformed his team with the former Shanghai, Henry O. Godwinn. With Tex and Shanghai, Tex was the clear "leader" IMO. The opposite was true with the Godwinns. By virtue of having more WWF experience, Henry (Shanghai) seemed to "take the lead" this time around. Maybe because of that, or the gimmick itself, this incarnation of the team never really worked for me the way Tex and Shanghai did.
Later on, they became Southern Justice under their real names, Mark Canterbury and Dennis Knight. That version of the team seemed cool as hell, but it didn't last long enough for anyone to really be able to judge it. If I recall correctly, Knight suffered a career-ending injury after taking a botched Doomsday Device from the LOD. Not sure if that is how the injury really happened or if that was just the storyline explanation. Either way, that spelled the end for Mark Canterbury's career. (Or did Canterbury come back for at least a short spelll to feud with LOD? I seem to recall that, but I may be confusing it with some other angle.)
Knight continued for a few more years as a lower card singles wrestler - Mideon, Naked Mideon, etc.
Overall, I'd call this team a mixed bag, but I blame it more on the silliness of their WWF gimmick than anything the wrestlers themselves did. Dennis Knight and Mark Canterbury were pretty solid and effective together in the ring, I thought. What did everyone else here think of their various teams and gimmicks?