I became a little bike freak this summer, and I did a pretty big bike tour with my family (we did the "Tour de Mur" in Austria (that's where I live xD)) and we met lots of e-bikers. They were mostly people who were too old to handle biking there with only their own power. I think for those people an e-bike is the right choice, but if you are able to bike yourself without electronic aid, I would definitely recommend to choose a normal bike ;-)
In terms of exercise, a classic bike is the way to go, there is no cheating, just pedaling and exercising.
An electric bike is more of a convenience in my mind. It makes life a little easier, and will likely make the bike ride more enjoyable, but it will be lacking in physical benefits.
Another thing to consider is the cost. An electric bike will run more money in most scenarios, due to the fact that it's newer technology, and more intricately composed in materials.
I would like to have an electric bike. I do enjoy getting exercise with a classic pedal bike, but it would be nice to just cruise and enjoy an easy ride every now and then.
My choice will always be the classic bike because I can ride it and I love cycling.
But I can also understand electric bikes too. I've seen many elderly people use it and I know it's easier for them to use electric bikes instead of classic ones.
However, for a fit person it's better to use the classic one.