The differencce between wegde gate valves and slab gate valves.
The basic difference, as you can see now, is one seals against leakage using a force applied to a wedging action against the valve in a downward direction, the other seals by line pressure pushing the slab horizontally against the edge seal, I believe it has springs for secure sealing at low pressure.  Call up the reps and they will be all too happy to come in and tell you the advantages of each.
I don't have experience with Walworth valves, but I can say M&J are good valves.  
Slab gate valves are also usually more expensive than wedgegate valves.
From anecdotal evidence (ie hearsay), wedge gate valves can get "stuck" more often than a slab gate. I am guessing that "gunk" can get into the bottom of the seat, and not allowing the wedge to seal tightly.

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