Actually, PNG supports 16 bit channels (as well as 1, 2 and 4 bits for paletted or greyscale images). TIFF meanwhile is kind of a kitchen-sink container format, so you can do quite a bit of strange things with it (store JPGs inside it, support tiling), but I don't think many viewers support everything in the TIFF standard.
> The standard allows indexed color PNGs to have 1, 2, 4 or 8 bits per pixel; grayscale images with no alpha channel may have 1, 2, 4, 8 or 16 bits per pixel. Everything else uses a bit depth per channel of either 8 or 16.
https://en.wikipedia.org/wiki/Portable_Network_Graphics#Pixe...
> TIFF is a flexible, adaptable file format for handling images and data within a single file, by including the header tags (size, definition, image-data arrangement, applied image compression) defining the image's geometry. A TIFF file, for example, can be a container holding JPEG (lossy) and PackBits (lossless) compressed images. A TIFF file also can include a vector-based clipping path (outlines, croppings, image frames).
https://en.wikipedia.org/wiki/TIFF#Features_and_options