The problem with these types of dogs is that genetics does not work that way. When you mix two breeds, you don`t necessarily get the best of both dogs.
What is the best of both dogs anyway? When you mix a lab and a poodle, which traits are you hoping to get? As a fan of Labs, my ideal mix would be more lab, but others may not feel the same.
To go back, the "labradoodle" started when a man tried to mix a Lab and Poodle to create a hypoallergenic service dog. No one wanted a mix, so he started calling it a breed, the "labradoodle". It took off from there. The problem is, he was never successful at reliably breeding the low dander coat of the Poodle into the pups.
He is credited with starting this whole "designer dog" thing although the cockapoo has been around longer.
His story is here
http://www.readersdigest.com.au/content/printContent.do?contentId=43132
When you mix two breeds, you end up with pups that can be any mix of the two breeds. There is no consistant coat, size, temperment, drive, color, etc within even the same litter. It is NOT the best of both breeds. It can be the worst of two breeds, or any mix thereof.
As for a second generation mix, If you take a mix and breed it with the same type of mix (called second generation breeding), you will find that they sort of start to sort themselves out into the original breeds with a few traits of the other breed mixed in, again completey random. Most "designer dog" breeders admit to staying away from this type of breeding because of the wide variation it produces.
Many breeds did originate from mixing breeds. The difference is that they were selectively bred over many many generations for particular traits with a goal in mind until they consistantly appeared, that is, bred true. This takes a strong understanding of genetics and a consitant breeding program. "designer dog" breeders rarely go past a second generation and have no specific goal they are breeding towards.
Here is a link showing the wide variation of the mixes of Labs and Poodles. This site also states that they do not typically go past the second generation as I have mentioned.
http://www.goldendoodles.com/faqs/generations.htm
What it all comes down to is most "designer dogs" are no different than the average mixes in your shelter, only there is someone breeding them intentionally and charging a fortune for it. Many of these breeders tell lies like the one you have heard about getting the best of both breeds. They also make claims of "hybrid vigor" which is untrue (hybrid are a mix of two different species like horses and donkeys create a mule, breeds are NOT different species).
The "labradoodle" you pay $2000 is no different than the Lab/poodle mix in your shelter. That goes for any of the other "designer' mixes you get.
Add-
"Puggles" are the most ironic mix of all, you take a breed with known breathing issues and breed it with a SCENT hound with high energy. LOL.
@Pekesrule - I fully understand where some purebreds came from and addressed it in my answer. It takes many many generations to create a new breed. These "designer" breeders rarely go past the second generation. They will NEVER breed true if that continues.
And these people breeding this dogs do not have a clear vision of what they are producing. What is the ideal size, color, coat, etc? That can vary from one person to another. With purebreds that were once mixes, like the German Shepherd, their work dicated this, form followed function. Their coat was dictated by the weather they worked in, the size was needed to be big enough to do the job, but small enough to be sustainable, even the black back was bred for to help identify the dog among the white sheep.
What function does a puggle have?
As for the breeding for allergy friendly dogs, that did not succeed. The man who started out with that idea abandoned his breeding program. It has continued, but they still have not been able to consistantly produce the low allergy coat of the poodle in these mixes.
I don't believe for a second none of these dogs are in shelters near you. They may not have their fancy name, but they are there.
And for the record, I am not against anything new. I am not even against creating new breeds for a purpose (stress on the purpose), if it is done right. That is with a clear goal and a breeding program to achieve it. I am against mixing two breeds, calling it a new one and charging a fortune for it.
What is the difference between the pug/beagle mix at the shelter and the $1000 "puggle" from a breeder? There is no difference.