My first Everdrive was the Everdrive 64. It was long the most useful Everdrive I had simply because of it's high compatibility and because N64 emulation was (and still is) in such a bad state. Thanks to the ED64, I could suddenly play all those games I could never get like they were meant to be played on the real hardware, and without all the bugs and inaccuracies of N64 emulators.
But it's not really my favourite system so I won't cast my vote on that. Nowadays, thanks to the Everdrives and other flashcarts, I hardly ever use emulators anymore on any system I own, except for quick testing.
I own Everdrives for most of the systems, and the Everdrives I use the most are the Everdrive N8, SD2SNES (although not exactly an Everdrive), the Everdrive GB and the Turbo Everdrive v2. The Mega Everdrive Pro will probably also enter this list once I get it.
For it's large and unreplaceable game library, thriving homebrew scene and simple yet versatile and balanced 8-bit hardware, I say the Famicom and the Everdrive N8.