The main difference between a solid-body electric and a hollow-body acoustic-electric is that solid-body's are far more capable of having higher gain through the amplifier.
You can also use it with more effects, including distortion, which would have feedback issues for an acoustic-electric.
I think it may also depend on the quality of the pickups, but in my experience, solid-body electrics have more sustain than an acoustic-electric through an amp.
This may be because the solid-body allows more vibration to be transferred to the undersaddle pickup (theoretically), and that they are
made to be played primarily as electrics.
For example, Risa's nylon-string electrics have been set up in a way that is not possible for an acoustic, for the purpose of sounding good electrically.
I think the electric-aspect allows the solid-body uke to be able to blend in better with conventional music, as playing it through a guitar amp will make it sound a bit guitary.
I see this as a good thing.
Aside from sound, another reason why I like electric ukes is their portability and durability. There is so much potential in such a small package.
A steel string electric has more sustain and crispness to the tone.
Kinda hard to explain in words, but I suppose it's like comparing a steel-string electric guitar with a classical guitar.
You can distort with a nylon-string electric quite well, but it won't have as much sustain or sound as badass as a genuine steel-string electric.
Afterall, nylon strings and piezo pickups are widely used in acoustic instruments. I wonder why there are so few solid-body nylon string guitars
However, a nylon-string electric retains its ukulele-heritage more strongly than steel strings. The feel of the strings, tension and clean-acoustic sound is closer to an acoustic uke.
Steel string electric ukes step closer to the electric guitar family. It's still an uke, due to its tuning, but if you've never played steel-strings before, it'll take some getting used to.
For purely electric applications, I prefer steel-strings. I find them more practical for my uses, where I'm playing along in a band with conventional instruments like guitars, keyboards and drums.
Nylon string ukes, in my opinion, are not as versatile due to their shorter sustain and punchiness.