I personally like the "they live here, you don't."
Training, well, we did it all. We took our dogs to puppy kindergarten, and we didn't keep working with them...time passed quickly and the poor dogs were getting pretty much, well, at home. (Their house, not ours.)
Then we hired an expensive trainer to come to our house, one on one training. We didn't follow through and so it didn't work either.
It dawned on me that we were really bad parents. Our intentions, as good as they were, didn't cut it. We needed to get them trained AND FOLLOW THROUGH! (But we wanted them to feel at home and comfortable, not restrained and forbidden.)
We finally sent them to what we called "doggie boot camp" and they stayed (all 3 of them) for a week. When we picked them up, they were absolutely perfect! The training worked wonders, they had so many good manners it was scary.
This time, we try to follow through. Sure, sometimes we don't...but when our dogs misbehave (which they don't really, not any more) it is because they are doing what dogs do.
Dogs are not human, they don't do things for spite or because they are mad at us...the do things because they LIKE what they are doing! Pleasure. It's that simple. Dogs like to chew, bark, dig, tear fluff out of sofas, jump on their people, nip and play, roll around on the ground, chew up favorite shoes, shred papers, discover stashes of forbidden things...and they like to be loved.
They will do just about anything we want them to do, as long as they know what that is. They need short, quick commands that they hear often and ones that they learn the meanings to. And they need to know that if they don't do it, there will be consequences (whether it is not getting a treat, a click, a love, or whether it is a quick tug on a prong collar.) I don't believe in being mean. I think that dogs learn love and kindness by the way we treat them...they also learn aggression and fear by the way they are treated.
They rely on us to be consistent. We can't let them chew on old shoes if we don't want them to chew on new ones. They don't know the difference...so, what I have learned is that the training needs to come FROM us...and WE need to be trained to do it. Most importantly, WE need to keep it in mind 24/7 until it is automatic for us and for our pets.
So, I can't say what type of training works best (although for us a prong collar does the trick). I have seen some wonderful dogs (well behaved, gentle, quiet) living with old ladies who give them treats from the kitchen table and I have seen really bad dogs living with aggressive and restrictive people...I think that it boils down to...you have to learn how to communicate with your dog, then let your dog know that you will be consistent. That you are the top dog, but you love them very much.