Allow me to add my 2 cents (and as I like to say, it's in an E*Trade account, so now it's worth even less ...):
* I've recorded into a Roland VS880 -- 18-bit converters, 24-bit mixing section, 16 bits actually stored on the hard drive
* I've recorded into
an Echo Gina 20, which is a PCI card/break-out box (with converters in the box for reduced noise issues than if they were on the card) with, as the name implies, 20-bit converters.
* I've recorded into a Pro Tools Digi 001 as well as
a Digi MBox, both 24-bit converters.
* I've bypassed the converters of all the above gear by going SPDIF thru the 24-bit converters in
my Mindprint DI Port.
What I've found is, the farther down this list I went, the better the sound quality became. Unquestionably so. AND, it proved to me that the bit resolution at which data's stored is just as important as the bit resolution of the converter capturing the sound into the system -- the DI Port was a vast improvement over the VS880's stock converters, but the DI Port through the PC into a 24-bit session was much better. This was true even when the 16-bit sessions in the Roland were in their "uncompressed" data mode (meaning, actually 16 bits .. it's this weird thing Roland does in some recording modes but not the mode I tested, intentionally).
It also proved to me that the quality of converters of the same bit resolution can affect the sound, as can the pres/gain stage.
I typically record in 24/44.1, then use the dithering algorithms in my software (PT LE) when making a stereo master. It sounds better than not dithering and better than a 16-bit session, in my case.
I hope this is useful.