Soundwise
Using 24-bit FLAC to export 24-bit project preserves audio data, whereas converting to 16 or even 8 bit will reduce audio data. Sound deterioration may or may not be noticeable, depending on source material and number of other factors.
That is true for wave files, of course. The paradox that had me perplexed is that if FLAC is lossless regardless of what options are chosen, then why are there options? I think I have resolved that conundrum, at least to my own satisfaction. I was just thinking about it all wrong.
Looking at the
file format spec, FLAC supports 8, 12, 16, 20 and 24-bit sample sizes and most standard sample rates. That triggered an epiphany: FLAC perfectly preserves data
as it was encoded.
When, for example, I export 32-bit floating point data from my SONAR project as FLAC, some data will in fact be lost as a result of wordlength reduction (FLAC doesn't support floating-point data). Similarly, if my project is 48 KHz and my FLAC sample rate is 44.1KHz, then there will also probably be some data loss.
However, these data losses happen prior to the actual encoding process,
after which data is preserved with 100% accuracy.
I exported a project to both 8- and 24-bit subformat FLAC to see if I could discern any subjective difference. The 8-bit subformat produced a much smaller file (6MB vs 42MB vs 62MB uncompressed). However, it also had the high noise floor you'd expect from 8-bit data's reduced dynamic range.
So to answer the OP's question, use the 24-bit subformat unless you're sending the file to someone who has explicitly asked for something else.