The image bits are identical. This is a metadata issue. This image file contains lots of metadata (Xmp, Adobe, unknown, etc.) and this metadata contains two color profiles/spaces/contexts:

1. ProPhoto RG (usually found in C:\WINDOWS\system32\spool\drivers\color\ProPhoto.icm)
2. sRGB IEC61966-2.1 (usually found in WINDOWS\system32\spool\drivers\color\sRGB Color Space Profile.icm)

The problem occurs because the two contexts order may differ in the target file for some reason. An image viewer can either use no color profile (Paint, Pain3D, Paint.NET, IrfanView, etc.), or use (from my experience) the last color profile in the file (Windows Photo Viewer, Photoshop, etc.).

You can fix your issue if you clone the frame, ie:

var frame = BitmapDecoder.Create(new Uri(inputFilePath, UriKind.RelativeOrAbsolute),BitmapCreateOptions.PreservePixelFormat, BitmapCacheOption.None).Frames[0];
var encoder = new JpegBitmapEncoder();    
var copy = BitmapFrame.Create(frame);
encoder.Frames.Add(copy);
using (var stream = File.OpenWrite(outputFilePath))
{
    encoder.Save(stream);
}

As in this case, the order is preserved as is.

If you recreate the frame or transform it in any way, you can copy the metadata and color contexts like this:

var ctxs = new List<ColorContext>();
ctxs.Add(frame.ColorContexts[1]); // or just remove this
ctxs.Add(frame.ColorContexts[0]); // first color profile is ProPhoto RG, make sure it's last
var resized = BitmapFrame.Create(new TransformedBitmap(frame, transform), frame.Thumbnail, (BitmapMetadata)frame.Metadata, ctxs.AsReadOnly());
var encoder = new JpegBitmapEncoder();
encoder.Frames.Add(resized);
using (var stream = File.OpenWrite("resized.jpg"))
{
    encoder.Save(stream);
}

Note an image that has more than one color context is painful (and IMHO should not be created / saved). Color profiles are for there to ensure a correct display, so two or more (rather conflicting! sRGB vs ProPhoto) profiles associated with one image means it can be displayed ... in two or more ways.

You'll have to determine what's you're preferred color profile in this strange case.