One of the greatest inventions in the motorcycle industry in my opinion is the Dual Sport, sometimes referred to as an On-Off Road Bike. These bikes initially were off road machines or trail bikes that had lights and blinkers attached to them to make the vehicle Legal for road use. The early models had a bigger stator for more output to run the added lights but were not much different than their dirt bike sibling. The tires had less aggressive tread patterns but in all actuality the XR model (dirt) was not much different than the XL model (street).
Over the years things have changed as emission laws tighten and rider expectations grow. You can still find those same dirt bikes with the legal modifications by looking to Husqvarna or KTM and you will pay a premium for those bikes as well. Other manufacturers have taken a different route and tried to make the bikes a bit more on road capable by sacrificing the off road capabilities. Honda and Kawasaki have both produced an entry level bike that has been criticized by some for their off road capabilities.
If you are looking for an off road bike for your aggressive riding that you can ride to and from the trails I would point you in the direction of the KTM and Husky models. If on the other hand you are looking for a bike that can get you to the trails and your going to explore leisurely then buying the Honda or Kawi for half the price will work just fine. As with anything in the motorcycle market once you get away from the task specific bike and venture into the dual purpose you will be making sacrifices in one task or another or sometimes both. In most if not all cases the Dual Sport will not perform as well at off road riding, as a dedicated off road model bike. On the flip side it will also underperform compared to an on road only motorcycle.
What the Dual Sport does is allow you to leave your house on the bike and not truck or trailer to a place to ride. This gives you the freedom to go to another place by riding and not loading up and unloading when you get there. It opens up the world of exploration on and off road and depending on your riding abilities and riding style there is a bike for just about everyone.