They run the game directly via the original hardware so certainly better than an emulator. But not all Everdrives support all games - especially if the original game used a unique chipset. With some systems this isn't much of a problem - the Everdrive may work with 99% of the system's game library. With systems that often relied on enhanced carts - like the Super Nintendo - the compatibility rate is lower. Beyond this, saving can sometimes be a little tricky depending on the system. Like, having to reset the system before turning off the power or something. Not a deal breaker by any means.
My biggest disappointment is with hack compatibility. I was really hoping to play some quality hacks on original hardware but many are incompatible and/or very buggy beyond any inherent hack-induced buggy-ness. Some can be patched but others rely too heavily on emulator specific code, apparently, so won't run on the actual original hardware.
Which kind of flies in the face of it actually being emulation, I suppose.
A shame, really. Would love to find a Everdrive/hack compatibility resource someday.
This isn't necessarily the Everdrive's fault - they're not advertised to be hack compatible. But keep this in mind if you were hoping to play lots of popular hacks in addition to original games.