From the perspective of on-street riding, the question often comes up as to whether or not prior off-road riding experience is beneficial or harmful. Invariably I fail to satisfy the questioner because my answer is 'both'.

There should be no doubt that off-road experience provides an opportunity to learn great skills in the handling of a motorcycle, particularly for those situations where traction is less than optimal or when the bike is close to its limits (big lean or during obstacle avoidance.)

On the other hand, off-road experience tends to be irrelevant when it comes to having to deal with traffic or motorway speeds and driving.

It is generally true that off road riding involves an increased expectation of accidents. Spilling (dumping) a bike off-road happens with some frequency. On-road motorcyclists expect to never have such an accident. 

Except when racing, off road riders that experience an accident can be virtually certain that they were responsible for it. On-road driving accidents are about equally the responsibility of someone else as of the motorcycle rider. 

On a more subtle note, off-road experience tends to result in riders who become convinced that they, unlike all the 'squids' out there, are more likely to survive riding motorcycles on the street. This, in turn, tends to lead to these riders being more willing to ride closer to 'the edge' - taking risks that others shy away from.

Of the surveys that I have conducted here on the site it is clear that those who ride dirt tend to have slightly fewer accidents than those who ride street, but when you add any form of racing (motocross, for example), they have the highest incident of accidents, by far. (By the way, those who ride dirt have many more accidents, but not as many accidents that involve injury or death - probably because they tend to ride with far superior protective gear such as hard armour.) 

When you have off-road experience you are unlikely to be intimidated with unpaved roads or even riding on hard packed sand.

One interesting observation that my site surveys have shown is that riders who have off-road experience tend, almost universally, to wear a helmet when they ride on the street. (Bravo!)