The ENC28J60 chip based shields isn't compatible with the (official arduino) Wiznet W5100 based shields.
There are a few arduino libaries around for using for the ENC28J60. It would be best to search the arduino forums.
The ENC28J60 doesn't have the TCP/IP stack built into the hardware like the Wiznet, so the cost is it takes a lot more effort and SRAM on the arduino to run it, as you have to implement it in your code/library. But it's still usable for small applications.