You may not need to use all 24 bits, but too low an analog signal into an A/D converted can be a problem. You could be using only the lowest 10 bits of your 24 bit hardware, and that would certainly degrade a 16 bit source.
The performance of my Behringer DEQ2496 equalizers was definitely improved when I adjusted analog gains to as to fully drive the 24 bit hardware in them. (Gain before the DEQ2496 was increased, and gain after the DEQ2496 was reduced, so that the overall gain was the same, but the signal was stronger as it went through the DEQ2496).
The performance of my Behringer DEQ2496 equalizers was definitely improved when I adjusted analog gains to as to fully drive the 24 bit hardware in them. (Gain before the DEQ2496 was increased, and gain after the DEQ2496 was reduced, so that the overall gain was the same, but the signal was stronger as it went through the DEQ2496).