there are 2 different things going on in this thread. as "notlance" said, going from a higher sampling rate to 44.1 is resampling, while going from a higher bit rate usually involves adding dither (without dither it's just called truncation).
if you want to record in 44.1, go ahead. But if your recorder can record at 24 bits, I recommend that. It gives you much higher headroom. You can run the levels lower and still be using more than 16 bits. If you record at 16 bit, you really need to be cranking your levels to get close to 16 bit resolution.