Here's the lowdown:
TIFF by itself is just an image format. By itself, it is lossless.
The reason I prefer using 16 bits/colour (48 bit TIFF) is this. When you have 8 bits/colour/channel, each channel has 256 possible values, whereas a 16 bit/channel image gives you 65536 possible values. When you do any sort of image manipulation (curves, levels, colour balance, etc) you lose data. 8 bit images are much more prone to posterization and colour banding.
To illustrate, just try this: Scan in an image in 16 bit format. Make a copy and convert it to 8 bit/channel. Do some massive editing, curves, levels, colour correction, etc. Now open up the histogram tool and look at the lost chunks in the 8b/ch image.
As for file formats, TIFF images can be uncompressed (aka RAW) or compressed. TIFF compression can be lossy or lossless. LZW or ZIP TIFF compression is lossless. TIFF images can also be JPEG compressed, and can be lossy. JPEG can also be lossless, but the image size becomes huge and you might as well save it as a TIFF file. However, JPEG images are 8 bits/channel. I'm not sure about JPEG-2000 though.
To illustrate JPEG's lossy compression, take a TIFF image, make multiple JPEG copies of it, saving at 90%, 80%, ... 10% quality. Now look at the artefacts and jaggies in the JPEGs.
TIFF by itself is just an image format. By itself, it is lossless.
The reason I prefer using 16 bits/colour (48 bit TIFF) is this. When you have 8 bits/colour/channel, each channel has 256 possible values, whereas a 16 bit/channel image gives you 65536 possible values. When you do any sort of image manipulation (curves, levels, colour balance, etc) you lose data. 8 bit images are much more prone to posterization and colour banding.
To illustrate, just try this: Scan in an image in 16 bit format. Make a copy and convert it to 8 bit/channel. Do some massive editing, curves, levels, colour correction, etc. Now open up the histogram tool and look at the lost chunks in the 8b/ch image.
As for file formats, TIFF images can be uncompressed (aka RAW) or compressed. TIFF compression can be lossy or lossless. LZW or ZIP TIFF compression is lossless. TIFF images can also be JPEG compressed, and can be lossy. JPEG can also be lossless, but the image size becomes huge and you might as well save it as a TIFF file. However, JPEG images are 8 bits/channel. I'm not sure about JPEG-2000 though.
To illustrate JPEG's lossy compression, take a TIFF image, make multiple JPEG copies of it, saving at 90%, 80%, ... 10% quality. Now look at the artefacts and jaggies in the JPEGs.