A raster has four types of resolution - spatial, spectral, radiometric, and temporal. The pixel depth is under the radiometric resolution of a raster. It simply specifies how well the differences in brightness in an image can be perceived. The higher the radiometric resolution (pixel depth), the better small differences in reflected or emitted radiation can be measured. It also means that you'll have a larger volume of measured data.
However, unlike image data, computer monitor screen pixels can only have 256 unique RGB brightness values. Clearly, this limitation prevents the most of the data from being displayed with brightness exactly equal to their real value. Here you can use image enhancement like contrast stretching to achieve a better rendering of your raster.
So when to use 16-bit:
- if you want to perform spectral analysis on your raster
- if you want to create a visually appealing final product
- if you want maximum clarity on areas covered by shadows and haze
8-bit:
- if you prefer smaller file sizes
- if your software has file limitations (say, can't open 16-bit rasters)
- if you will use your raster as a backdrop