export line work issue

I auto aligned the two versions, and set the top one to Difference, and they are are close to identical, with just the tiniest change showing around the star.

When line work really does get lost, and so long as it is on its own layer, try copying the layer and set to Multiply.

You may find that PNG works better for this kind of image.

The PNG format is designed for graphics with flat colors, whereas the jpg format is designed for continuous tone photographs.

It uses lossless compression, so it should be identical to the original.

In any case, always view the image at 100% as suggested by @D Fosse 

This is the only view that will present you with a true rendering of the image. Any other view will be inaccurate and misleading because the image has been scaled.

Set View to 100% (ctrl+1) and check again.

100% is a very significant number. It has nothing to do with size. It means that one image pixel is represented by exactly one physical screen pixel.

It's the only way to see the actual pixel structure of your image faithfully, pixel for pixel. At any other zoom ratio, the pixels have been resampled for screen. One screen pixel may now represent, for instance, an uneven fraction of a 3x3 pixel block in the image.

The thing is, none of this matters in a standard photograph. It will all be smooth gradations and more or less fuzzy edges anyway. But this is different! Here you have sharp pixel transitions and thin lines that may be only a few pixels across. In these cases you always need to view at 100% to see it correctly.

All this without even resizing your image. If you do that, the same principle applies, only then you will change the actual pixel data, not just how it's represented on screen.