Conformation dog shows have just about ruined many of the older breeds of hunting dogs. The Great Dane is one of them.
Instead of being bred for their hunting abilities the dogs have been bred more for looks - and for that matter looks that were deemed as being perfection for the breed by a bunch of people who themselves are not hunters and have no idea what a good hunter needs. This has resulted in dogs that are not what they would have looked like a hundred or two hundred years ago and of course dogs that are not capable of performing like the would have a century or two ago. The result is a great hunting dog that has been turned into a large obstacle to be maneuvered around in your home.
Take the labrador retriever for example... in the 80's the AKC began importing judges from Great Britain to guest judge their conformity dog shows and a lot of these judges judged labradors. British labs by then were no longer bred for sporting purposes but rather for a certain look. As a result they graded dogs that didn't have large blocky heads, broad chests and heavy set bodies with heavier legs and feet very poorly. This trend spread on to American judges since all things "Euro" were considered trendy and desirable.
Well at that point in time the "American" lab breeds were slender dogs with slenderer longer heads and smaller ears. They were excellent hunting and working dogs and were great at doing what they were bred to do - hunt and retrieve. What happened is that many breeders, in order to score high in conformity events, started changing breeding stock and bred these "British" or "English" breed labs. More and more the English/British breed labs are being bred and less the American or field breed labs - so much so that now the lab is embodied as a blocky headed, broad chested and stocky dog (English breed).
The problem here is that typically (there are of course exceptions) the English breed labs are not as good of hunters as the American/Field breed labs. They aren't as fast, agile or as determined a hunter as the Field breeds. They tire more quickly and tend to not have as good of noses. Personally I also find them to be more difficult to train for more advanced concepts... in otherwords I think they're not as smart as the Field breed labs.
Personally I won't own an English breed lab myself and try to steer others away from it.
Now back to Great Danes - this has obviously happened to them at some point in time however in a worse way. I doubt you'd be able to find a good hunting Dane without an exhaustive search and great expense.