Wiznet W5100 vs. Microchip ENCx24J600
The W5100 has a TCP/IP core on the chip. With the Microchip ENC devices the user has to implement a TCP/IP stack themselves, on the MCU that is interfaced to it. This is quite easy with a suitable PIC, as free TCP/IP stacks are available from Microchip.

The W5100 has the advantage that it can be used with virtually any MCU, but a fairly powerful device is needed to run a TCP/IP stack if an ENC chip is used.

Of course, another option is to use an MCU with a built-in MAC and PHY. Microchip makes some nice ones, and there are ARM variants with them as well.