Check the specs on the Ether device on your shield. I assume it's the wiznet W5100, and its SPI speed will be the limiting factor. I have a standalone W5200 and its SPI speeds are better (see Maple results in my table in earlier post in this thread), though I had to hack in DMA/SPI to get the best results on the Maple. (It's on my TODO list for DUE). The processor on the DUE has a builtin in Ether controller, but you'll have to wait for another kind of Arduino board that breaks those Ether IOs out -- and then you will need a lot of code/memory to do the TCP/IP protocols ... which is why the wiznet critters are attractive.