mol[n:_Integer|{_Integer..}, o_:"Pseudospectral"] := {"MethodOfLines",
  "SpatialDiscretization" -> {"TensorProductGrid", "MaxPoints" -> n,
    "MinPoints" -> n, "DifferenceOrder" -> o}}

molfem[measure_: Automatic] := {"MethodOfLines",
   "SpatialDiscretization" -> {"FiniteElement",
     "MeshOptions" -> MaxCellMeasure -> measure}};

Clear@solve;
tend = 5;
solve[opt_] :=
 NDSolveValue[{I D[u[t, x], t] == -D[u[t, x], {x, 2}] + I Sin[x] u[t, x],
   u[0, x] == Exp[-x^2] Exp[I x], u[t, -Pi] == u[t, Pi]}, u, {t, 0, tend}, {x, -Pi, Pi},
  Method -> opt]

soltraditional = solve@mol[200, 4]
solfem = solve@molfem[]

Plot[{ReIm@solfem[tend, x], ReIm@soltraditional[tend, x]}, {x, -π, π}]

Plot[{Abs@solfem[tend, x], Abs@soltraditional[tend, x]}, {x, -π, π}]