Generally, I record 16 bit, since I am passing audio (via lightpipe) thru an old blackface 16-bit ADAT as well as my Layla Card so I can get 16 tracks at one pass. However, after reading this last week, I did a session for a small group with only 8 live tracks so I ran it at 24-bit.
It sounds real good, but I can't honestly say I can hear a difference. I'm sure there is an advantage to running 24-bit...and so why not do it. But can you hear it? Not I.
sometimes getting higher quality headphones could help in hearing the difference, it might be something that your headphones can't hear
As PeterVred found out, recording 16bit generated sound (i.e. 16 bit A/D converters etc.) as 24bit has no immediate noticeable sound difference (the additional 8 bits are "empty" so contribute nothing). However, if you can maintain 24bit after recording through the post-production chain, there are some sonic advantages esp. where processing and mixing are concerned, where all calculations are done at a higher resolution.
Generally most video uses 24bit these days.
If the final delivery is 16bit, the 24bit should be correctly dithered to 16bit, but only at the final stage.
"sometimes getting higher quality headphones could help in hearing the difference, it might be something that your headphones can't hear"
Sony MDR-7506 units will do just fine and, with replaceable ear cups, they'll probably last the rest of your limited actuarial life expectancy.
Yes, the Sony MDR-7506 are almost a standard for production sound mixers. Very rugged and reveal dialog flaws and extraneous noise well. Other popular HPs for PSM's are the Sennheiser HD-25 and HD 280, and AT's ATH-M50.
From 16 to 24 bit, each bit is equal to 6 dB. So a 24 bit file recorded @ -48dB could be normalized to optimal levels without adding much noise. Otherwise, there is not much audible difference with proper levels, except in music and S/FX recording where the reverb tails and other low level nuances may sound a little muddy.