I own both an acoustic kit and an electric kit so I think I'm qualified to comment on this.
First and formost, if the term "electronic drums" makes you think of that cheesy '80's "pyew pyew pyew" synth sound forget about it. Those sounds were created manipulating a sine wave like an old school keyboard. Today you have samples of audio recorded from actual drums, and with MIDI you have access to all of the software libraries that keyboard players use as well as triggering lights or even video! The truth is you have already heard electronic kits and probably didn't even know it. Almost everything in the rock world these days has "sweetening" from a layered drum track using samples or triggers.
In terms of playability its much like an acoustic guitar verses electric. They are the same, yet slightly different. However with the right equipment you CAN do cymbal chokes, use brushes, or on the top V-Drum kit brain you can even compress your hi-hats by mashing on th e foot pedal and you will get that subtle pitch bend of the two plates getting smashed tighter together. It's pretty amazing.
Additionally, having an E-kit means you can change the sound of the kit from song to song in a cover band. For example, you can go from an open and midly Bonham sound for a Zep cover to a tighter modern sound for a Pantera tune, then finish off the set with some club track with a hip hop kit. It's pretty cool.
For the stage, going to E-Drums helps reduce volume wars between band members. Well guitarists may take some convincing

E-drums also require less stage real estate which allows more room for the rest of the band to breathe and move around, but more importantly it allows your band to fit in smaller venues and get more gigs you otherwise might not have a chance at.
The look may be a no-go for some people but companies like Pearl offer a "normal" looking acoustic kit for an E-kit. In addition there are companies that make custom drum shells for E-Drums such as Diamond Electronic Drums. Additionally you could always plant an acoustic kick drum out front and cover up the trigger pad.
There are down sides to E-kits, and crappy power is one of them. If the club has shakey power you could fry your "drums" just as quickly as you pop a fuse on an amp. Power conditioners are a must.
I like E-kits but I also love A-kits. They are both awesome, just like a double bass is cool like a P-bass is cool.
Well I hope this helps, and for those of you that are maybe just starting to consider an E-Kit, take a closer look, and don't be afraid of what other's might think. You may be pleasantly surprised.