The equivalent would be a Leonardo with a W5500 Ethernet shield on it. Those shields are a bit less common than the W5100 shields but they are available.
There is a library that supports W5100/W5200/W5500 and automatically detects which one is used here:
The API will be the same as the Ethernet2 library. It's primarily intended for the Teensy boards with less effort put towards the standard Arduino boards. The Teensy 2.0 uses the same ATmega32U4 chip as the Leonardo so maybe that would be a good sign for you but I have no experience with Teensy so I can't say.