As I had a lot of riding footage laying around, I wanted to do a side by side comparison of the differences and similarities of "Dirtbike Riding and Street Riding". I have strong feelings that if you really want to become a better rider in general you should try and do both. Not everyone is as fortunate to have access to both, but if you do, here's why I think you should do it!
Teaches you the basics of riding in a "typically" less dangerous environment. No cars is a main highlight. You can focus on what it's like to lose traction, with the front, rear, or both tires at speeds that are less likely to break your neck. Feeling the rear slide out as you power on the throttle with a dirt bike is amazing. Dirtbikes are lighter then any street motorcycle and generally will make horsepower between 5hp all the way up to 50hp. Anywhere in the middle of that power range is plenty to have fun.
The main highlight is getting to see new places! It allows you to travel around, check out new spots on the map. There's a lot more traction and you go a lot faster. You'll learn how to work with the bike by leaning off in the corners. More weight does come with the benefit of more power and more stability.
Riding on the dirt will help develop the sometimes un-natural instincts need to stay calm in a situation on the street where you lose traction. Street riding will help you with bending the bike under you and being smooth on the throttle. Mostly they're just fun and here's the video to prove it.