You're not accurately paraphrasing me.
I think there's a lot more in play than the bit depth. Sample rate has a lot more potential to be significant, and it's also possible that there are mastering differences between 44/16 and 96/24 bit versions. Not to mention whatever was done to convert between the two sample rates.
But 16 vs 24 bit is pretty simple. 24 bits is a godsend when recording, and once done, can be effectively translated back down to 16.