Once again this is a very complex answer, which is one reason why volume print labs don’t want these. A 16bit tiff file holds way more information is the simple answer. And yes that’s a way larger file which is why volume print labs want the much smaller 8bit jpeg.
Many Photographers have heard it’s much better to shoot in Raw than it is in Jpeg. The key reason is because in Raw you get all of the information into your file. If you shoot jpeg? That destroys 80% of the information, and many things such as white balance can no longer be completely edited in the Digital Darkroom.
A 16bit tiff file allows for 281 trillion color combinations. An 8 bit jpeg can display only 16.7 million colors. If you did the math that’s considerably less colors. Most people do not think in trillions. However when it comes to photography these colors are important if you wish to obtain the best possible results. Even with Black and White.
When it comes to a printed image those additional colors will reduce banding. Banding in the sky can be seen in the image above. 16bit images allow for greater flexibility when editing, and also produce the highest quality prints possible.