I think mixing breeds in general is a bad idea for two reasons (A) You cannot be sure what characteristics you will get and (B) they are never the best examples of their breed.
People do it to try and have the 'best dog possible,' because they want the 'best characteristics' of those dogs. There's something about either the Bernese or the Golden they dont like - right? Otherwise they'd have bought the pedigree. The problem is, you very often don't know what you are getting. You could end up in a situation (which many people have) where you have the worst traits of two breeds. It's why rescues such as Spaniel Aid are so full of these 'designer doodles.' With pedigree breeding, it's easier to know what you're getting - particularly if you use a good breeder.
I see the argument a lot that it results in healthier dogs. But, as I mentioned above, this isn't true. I've just had a litter and the girl I bred from has a 3/3 hip score (which is excellent - breed average is 18 altogether, and hers is 6 altogether - and I have never seen a dog with better in 20 years of being involved in the breed). I have spent years breeding Goldies to have the healthiest dogs possible. I would never, ever, use her to breed anything other than Goldies. I breed to make my breed better and so do all the breeders I know that I would recommend (and those are the breeders with the healthiest dogs). That means that the sorts of dogs that are used to breed mongrels (for lack of a better phrase as we're not talking doodles anymore) are never the best examples of their breeds. They're not the healthiest. They're not the best bred.
People say that mixing breeds means you avoid possible things like dysplasia, but as I've shown above, that's also not true. Bernese and Goldies are both prone to cancer, dysplasia and heart disease. Breeding the two doesn't lessen the risk of your dog developing any of those issues. In fact, it makes it harder to find out how health your puppy might be because chances are you can't find generational health tests (which, although I have many issues with the KC - they do make it very easy).
With a pedigree, you can be more certain of health tests being done generationally. For example, I provide 3 full generations of health tests and a further 2 generations of 'mostly complete' - as heart tests weren't really done ten years ago and although that still means my dogs are fully health tested under KC requirements, they're not in my eyes as heart defects in Goldies are quite serious.
But with these other mongrels (again for lack of a better phrase) most often you might get the parents, but they won't be the best of the breed, and you almost certainly won't get grandparents. It's like humans: just because the parents are healthy, doesn't mean the grandparents were.
I would say, in theory I have nothing against these breeds. But I hate the idea of dogs being used for breeding that aren't the best example of their breed and where the breeder is negligent in choosing the sire/dam - we have enough defective dogs in the world, we don't need more!
Sorry that was a lot...