Legally, dogs are considered property, so "owner" is technically correct.
The term "guardian" is something that AR groups espouse, because they don't believe in animal ownership. Taken to its logical extreme, this means that we should not keep animals as pets, either. Some AR groups downplay this fact, others proclaim it proudly, but none of them deny that this is their ultimate agenda.
Since "guardian" is the word AR groups want in place of "owner", it is something of a hot-button word for a lot of dog people. I don't agree with the AR agenda, so I won't use the term "guardian" to refer to dog owners.
The way I have used the word "guardian" is when someone other than the dog's legal owner is looking after it--in my case, I have a breeding bitch for Independence Guide Dogs. She lives with me but I do not legally own her, so I refer to myself as her "guardian owner". It carries the same day-to-day responsibilities as being a legal owner, but technically, I can't claim her as "my dog" until she is retired from breeding.
I might have to find a different term for this, however. I've recently seen some 'doodle breeders advertising for what they call "guardian homes", which is the same thing as I'm doing--keeping and feeding a breeding dog owned by someone else--except that instead of a nonprofit guide dog program getting the puppies, the breeder gets them back and sells them for profit.
I could go on about that, but that's not the subject of this thread.