Tiff and DNG are effectively one and the same. DNG is tiff with a handful of adobe LR specific meta data tags. Adobe owns the tiff specification. Tiff tends to have better compatibility than DNG as not all software actually supports all the DNG tags.
in terms of bit depth, 16 bit per color is fine and has wide support. You won’t see a difference with a higher bit depth with current display and print technology, and that is very unlikely to change enough to make a difference any time soon.