It all depends on how you build the bike. I just converted a nice road bike by adding a geared rear hub motor. The geared motors (vs. direct drive) have a freewheel built in so they don't slow you down when pedaling (direct drive hub motors have a cogging effect when there is not electricity). And a geared motor is smaller, therefore less weight. In fact, I still road the bike normally after putting the hub motor on, since I had to wait another couple weeks for the battery to ship.
And, you can get the same cardio per unit of time (if you want) on an ebike as a regular bike. You just go faster, therefore further. And since you have a bit more speed, and you aren't required to do a major workout on every trip (so you don't have to change into cycling clothes), you end up using the ebike for a lot more trips -- therefore getting more exercise overall.
In my case, I have a 25 mile commute -- no way to make it in time on a regular bike. But an ebike makes it no problem. And I still get a decent amount of exercise (basically the difference between going for a very long walk vs running a sprint, so a different type of exercise), and on the weekends I give it my all (and just rack up more miles).