Using fewer mesh lines, 3D graphics

The FEM package will tend to give you more isotropic triangles as shown in your spherical mesh than other discretization functions in Mathematica. Also, for a torus, an implicit region seems to give a cleaner mesh than a parametric region as can be seen by the FindMeshDefects function.

Below, you can see a comparison between ParametricRegionand ImplicitRegion:

Needs["NDSolve`FEM`"]
torus = ParametricRegion[{(3 + Cos[v]) Cos[u], (3 + Cos[v]) Sin[u], 
    Sin[v]}, {{u, 0, 2 π}, {v, 0, 2 π}}];
mrtorus = 
  MeshRegion@
   ToBoundaryMesh[torus, "MeshOrder" -> 1, MaxCellMeasure -> .1, 
    AccuracyGoal -> 1];
HighlightMesh[mrtorus, 1]
FindMeshDefects[mrtorus]
torus = SolidData["SolidTorus", "ImplicitRegion"][1, 3];
mrtorus = 
  MeshRegion@
   ToBoundaryMesh[torus, "MeshOrder" -> 1, MaxCellMeasure -> .1, 
    AccuracyGoal -> 1];
HighlightMesh[mrtorus, 1]
FindMeshDefects[mrtorus]

Change the MeshFunctions and Mesh and PlotPoints

ex1 = ParametricPlot3D[{(3 + Cos[v]) Cos[u], (3 + Cos[v]) Sin[u], 
    Sin[v]}, {u, 0, 2 Pi}, {v, 0, 2 Pi}, Boxed -> False, 
   Axes -> False, MeshFunctions -> Automatic, Mesh -> {{0}}, 
   PlotPoints -> {12, 8}];
reg = DiscretizeGraphics[ex1];
newedges = MeshPrimitives[reg, 1];
Graphics3D[Map[Tube[#, .05] &, newedges[[All, 1]]], Boxed -> False]