I know a lot of NASCAR fans, and frankly, I don't know a single one that watches the races for the crashes.
One of the advantages that NASCAR has over drag racing is that it has an appeal to those who are not gearheads. I mean at a stock car race you really don't have to know much about the cars to appreciate and understand what is happening on the track. With NASCAR a person can attend a race for the first time and still get it without having to understand things like e.t.'s, the differences in car classes, etc.
But in the end there are probably a billion different reasons why some prefer one form of racing or team sport over another. For instance, I love hockey and find football to be very boring. I am in fact amazed that my fellow Americans could prefer the NFL over the NHL. Yet that certainly is the case. Likewise, those of us who prefer drag racing feel much the same way when it comes to NASCAR.
That's not the first time I've heard that... Seems to me a lot of drag racers and fans like what's considered an "alternative" sport, such as hockey. Find a hockey fan, and most likely you'll find a drag racing fan as well.
As to the perception of drag racing vs NASCAR, the casual fan does have a bit more of a hard time understanding the technical aspects and various classes NHRA has. However, restrictor plate racing, chassis adjstments, etc. etc. are also technical in nature and the average NASCAR fan knows all about this kind of stuff. The main difference as I see it is that NASCAR has slowly and gradually "brought the fan up to speed" as to the technical side of things, and also during that process made the drivers the actual stars of the show. This has not been a quick process. Back when both sanctioning bodies were on an equal footing (the 70's...considered the "good old days" of NHRA), the perception of NASCAR was of "good ole boys racin' around in circles" and the fans were ridiculed and looked down upon. The hardcore fanbase was confined mainly to the Southern states and the resultant image was born. Back then, the "Great American Race" was the Indianapolis 500, not the Daytona 500.
NHRA's image at the time was more of an "outlaw" type perception (everybody thought drag racers were wild-eyed punks with no regard for safety..racing in the streets, etc. etc.), and that continues even today, when some stupid kid in a Honda takes out a couple of cars while street racing, what's it reported as? That's right... it's almost always reported as "Drag Racer kills 2 in illegal race" or some such claptrap like that. NHRA's upper echelon didn't get it then, and they don't get it now... and the result is they're always playing catchup to NASCAR.
The fans of each type of racing are for the most part very closed minded. Look at some of the responses here for an example... NASCAR fans are even worse. That's not to say that there aren't fans who like both, but there are far too many that don't. How to bridge the gap is the key, and I don't really have a solution except for some gradual "education" similar to how NASCAR has done it. Modifying the existing race structure (less time between rounds has been a good start) to create a television product that's similar will also help.
Aside from that, I don't have anything else to offer...