Performance of ImageApply

Your If codition is pretty simple and can be precomputed on all pixels more efficiently to generate a composition mask

mask = Binarize[ImageDifference[imageA, imageB], 0]

You can then use simple arithmetic to combine it

ImageAdd[
 ImageMultiply[ColorNegate[mask], RGBColor @@ {1, 0.8, 0.2}],
 ImageMultiply[mask, imageB]
]

Putting all together

fadeAndShine2[old_, new_, color: _?ColorQ : RGBColor[1, 0.8, 0.2]] := 
With[
    {mask = Binarize[ImageDifference[old, new], 0]},
    ImageAdd[
        ImageMultiply[ColorNegate[mask], color],
        ImageMultiply[mask, new]
    ]
]
fadeAndShine2[imageA,imageB]//AbsoluteTiming//First

(* => 0.012 *)

And

MinMax[
 fadeAndShine2[imageA, imageB] - 
  ImageApply[fadeAndShine, {imageA, imageB}]]

(* => {0., 0.} *)

You can try to use compiled code and apply it to the ImageData of your images:

fadeAndShine[old_, new_] := If[old == new, {1, 0.8, 0.2}, new];

cFadeAndShine = Compile[{{old, _Real, 1}, {new, _Real, 1}},
   If[old == new, {1., 0.8, 0.2}, new],
   CompilationTarget -> "C",
   RuntimeAttributes -> {Listable},
   Parallelization -> True
   ];

And here the usage example with timings:

imageA = Rasterize[Graphics[Table[Circle[{x, 0}, x], {x, 1, 25}]], 
   "Image", ImageSize -> 500];
imageB = Rasterize[Graphics[Table[Circle[{0.8 x, 0}, x], {x, 1, 25}]],
    "Image", ImageSize -> 500];

imageC = ImageApply[fadeAndShine, {imageA, imageB}]; // 
  AbsoluteTiming // First
imageD = Image[cFadeAndShine[ImageData[imageA], ImageData[imageB]]]; //
   AbsoluteTiming // First
ImageData[imageC] - ImageData[imageD] // Abs // Max

0.355039

0.035754

0.

imageA=Rasterize[Graphics[Table[Circle[{x,0},x],{x,1,25}]],"Image",ImageSize->500];
imageB=Rasterize[Graphics[Table[Circle[{0.8 x,0},x],{x,1,25}]],"Image",ImageSize->500];

data1=ImageApply[Function[{old,new},If[old==new,{1.,0.8,0.2},new]],{imageA,imageB}]//
  ImageData;//AbsoluteTiming

data2=Map[With[{old=#[[{1,2,3}]],new=#[[{4,5,6}]]},If[old==new,{1.,0.8,0.2},new]]&,
  Join[ImageData[imageA],ImageData[imageB],3],{2}];//AbsoluteTiming

data3=With[{old=ImageData[imageA],new=ImageData[imageB]},
  With[{k=Unitize[new-old]},Map[{1.,0.8,0.2}#&, 1-k,{2}]+new k]];//AbsoluteTiming

data1==data2==data3

{0.637831, Null}

{0.249619, Null}

{0.0957136, Null}

True