What has changed in the Template system in 10.3?

There seems to be an incompatible change to NotebookExpression. While I don't quite know how to fix your example, I went ahead and fixed my trouble, i.e. just some input cells which have to be evaluated and hidden. This can be achieved with the following button:

   Button["TemplateExpression Exorcist",
  Module[{cell},
   (* move from inside the cell to the visible cell bracket *)
   Do[SelectionMove[SelectedNotebook[], All, Cell], {10}];
   cell = (NotebookRead[SelectedNotebook[]] /. 
       Cell[BoxData[
          FormBox[TemplateBox[boxes_, 
            "NotebookTemplateExpression"], _]]] :> boxes ) //. 
     BoxData[{b_, "General", BoxData}] :> BoxData[b];
   NotebookWrite[SelectedNotebook[], cell]]] // CreatePalette

So a cell like this one (whichi works in a template in 10.2)

Cell[BoxData[Cell[BoxData[
  FormBox[
   TemplateBox[{RowBox[{
       RowBox[{"myreport", "[", 
         RowBox[{
           Cell[
            BoxData[
             FormBox[
              TemplateBox[{"\"var\"", "\"t0\"", "Named", BoxData}, "NotebookTemplateSlot"], 
              TextForm]]], ",", "\"novar\""}], "]"}], " "}],"General",BoxData},
    "NotebookTemplateExpression"], TextForm]]]], "Input",
 CellFrameLabels->{{
    Cell[
     BoxData[
      TemplateBox[{"EvaluateDeleteInput"}, "NotebookTemplateCellBehavior"]]], None}, {None, None}}]

is change to a working one (in 10.3)

Cell[BoxData[
 RowBox[{
  RowBox[{"myreport", "[", 
   RowBox[{Cell[BoxData[
     FormBox[
      TemplateBox[{"\"var\"","\"t0\"","Named",BoxData},
       "NotebookTemplateSlot"], TextForm]]], ",", "\"\<novar\>\""}], "]"}], " "}]], "Input",
 CellFrameLabels->{{
    Cell[
     BoxData[
      TemplateBox[{"EvaluateDeleteInput"}, "NotebookTemplateCellBehavior"]]], None}, {None, None}}]

This bug was fixed with V11.0.0 release.