Well if you are running WS2003 servers they are likely very old and not very power efficient. So new servers will be more modern and use less power, and likely much more powerful.
WS2003 is a 32-bit OS while Server 2008 and 2012 are 64-bit, so you can run a server with more than 4GB of memory, which means a much higher load can be put on the server. You can virtualize, consolidating many single-purpose physical Server 2003 machines into one physical machine.
The security in Server 2008 and 2012 is also considerably improved. In Server 2003, once someone breaks through your security they have pretty much free reign to run amok in the server. WS2008 and 2012 are more walled off internally, so a break in to one area won't necessarily grant them access anywhere else.