You might see some differences in details and colors between the two, depending on the photos. For the most part, the difference is very minimal.
Library and Develop should look the same so it doesn't matter which is being exported because it's the same image.
So your question is, if Library and Develop look different, which is the right one? My answer would be you can't tell so you need to fix things to Library and Develop are the same. There are multiple reasons why: bad monitor profile that causes Develop to render wrong usually with a color cast, bad GPU driver (turn off the GPU in Prefs / Performance) that probably causes Develop to render wrong, corrupted preview cache so the previews don't get updated, so Library is wrong, etc.