Why does it matter which one is newer? This is an industry where product should be chosen based on how well it meets your needs.
Essentially the difference between the two is that the DNS-323 has a USB port on the back that can be used to connect a printer, which can then be shared, or a UPS, so you can have the DNS-323 shut itself down properly during a power failure, and also a bit torrent client.
If any of those features is important to you, you get the DNS-323, if not, you can save yourself a few bucks and get a 321 - if it were me, I spend the extra and get the 323, just for the added flexibility.
The other features are pretty much the same - they use what is essentially the same software.
Oh - to answer your question - the 321 is newer. The 323 was released in late 2006, the 321 was released in 2008.