Barnes & Noble Will Repartition Your 16GB Nook Tablet (Upon Request)
If you read the fine print, you'll notice Barnes & Noble offering to repartition your 16GB Nook Tablet so you can have more space for your own content. It reads:
If you want to re-configure the internal memory of your Nook Tablet-16GB for additional personal storage, you need to visit your local Barnes & Noble on or after 3/12/12 for help in doing so.
B&N didn't specify how the storage will be configured after repartitioning, but it's probably a safe bet to assume you'll have at least 5GB for personal use, if not much more. For the sake of comparison, the 8GB model only reserves just 1GB for B&N content.
If you don't want to take your 16GB Nook Tablet into B&N to have it re-configured, you can always add storage via the microSD card slot, a feature the Kindle Fire lacks, or you could root it.