Here is a way:

ineq = 0 <= Subscript[u, a] <= 1 && 0 <= Subscript[v, a] <= 1 && 
   0 <= Subscript[u, b] <= 1 && 0 <= Subscript[v, b] <= 1;
FindInstance[setA == setB && ineq,
  {Subscript[u, a], Subscript[v, a], Subscript[u, b], Subscript[v, 
   b]}] // FullSimplify
inters = FullSimplify[setA /.
   Solve[setA == setB && ineq]]
Show[{ParametricPlot3D[{setA, setB},
   {Subscript[u, a], 0, 1}, {Subscript[v, a], 0, 1},
   PlotStyle -> Opacity[.5]],
  ParametricPlot3D[setB,
   {Subscript[u, b], 0, 1}, {Subscript[v, b], 0, 1},
   PlotStyle -> Opacity[.5]],
  ParametricPlot3D[inters[[1]],
   {Subscript[v, b], 0, 1},
   PlotStyle -> Directive[Thickness[.01], Red]]},
 PlotRange -> All]