One must be plugged into the wall to function (electric like the Hitachi) while the other just must be plugged in to recharge then it can be unplugged to use it (something like MiMi or the FunFactory Delight).
I prefer batteries actually. I wouldn't mind rechargeable, but I would worry about losing charge partially through, or noting being charged when I wanted it. I don't use toys a ton, so they'd probably never be ready when I wanted.
It depends on the vibe. I have one that's electric (Eroscillator Plus) and I absolutely love it! From my understanding, it's not as strong as some of the other plug ins like the Hitachi. I love having 100% power 100% of the time. Most of my toys are rechargable, but if they could all be electric, I would be very happy!