They are mainly designed with the same thing in mind, to emulate a game cartridge to run ROMs on an N64. Both signed and unsigned code. However the Z64 does have a few advantages. It has a much more advanced OS to manage ROMs.. You can alter their region, bit swap them etc, and also run game shark and other cheat codes, save everything to the zip drive.
The biggest advantage over the Everdrive however is that you can put any original game into the Z64s cart slot and make a ROM backup from it to the Z64s zip drive.
The other advantage is compatibility. Some games won't run on an Everdrive without an additional physical chip soldered on, from an original game cart, but then some others won't run. With the Z64 you can use multiple original game carts to allow more games to run.
You can also utilise the Z64s IDE interface and a newer custom firmware to replace the standard zip drive with an internal HDD, or even a card reader to use CF and SD cards instead.
The only reason I'm selling it is because I just don't use it any more. I tend to emulate everything these days because I don't have the room to have systems set up.
