Out of your options, definitely fetch.

I try to mix jakes walks up. He gets onlead walks when its too dark to go anywhere else. But usually its a walk in the park, where he can have loads of smells, chase the rabbits , play with dogs, play fetch, have a swim. I also sometimes throw his ball somewhere he has to have a good search to get it. He loves that! Or just a good run around the woods

Dahlia has NO interest in fetch beyond a couple half-hearted runs for the ball. She'd much rather walk, even on lead, where she can sniff and sniff and sniff some more!

I dunno about Molly but fetch tires me out more than walking! We can only play it for 5 minutes at a time because Molly only runs to chase & then leaves it so I end up tiring myself out running up hills to fetch balls that she's left behind!

In all seriousness though, I'd much rather do an hour's walk. Sure she might not run about as much or burn as much fat as she would playing fetch but she gets much more in the way of mental stimulation when we go for a walk & I certainly think that's more important than her burning some extra fat

As Axel doesn't 'do' fetch, it'd be an hours walking for me, tires him out mentally and physically

Actually, fetch in the house (for example) will burn just as much as running outside as the dogs heart rate will still increase enough to burn calories.

For my breed though 20 minutes of mind games will tire him out more than a 5 mile walk any day! I do make sure he has both every day though.

Well fetch as they are running, but to be honest I would never allow 1 hour of fetch with any of mine...soz they get approx 20 mins over the walk period of fetch the rest is swimming in the river and playing, then walking along side

our morning offlead on the field is a fetch, but I never more than 15 -20 minutes with a few rests in between to say hello & play with other dogs. An onlead walk is about 40 minutes & although she is more tired with the ball run, I think she gets as much satisfaction from both.
I find that at home, 10 minutes of "find it" wears Tilly out - with all that sniffing!!

Cain can't physically play fetch for an hour, he's knackered after chasing the ball maybe ten times max! Lol. Because I can't get him off lead as often as I'd like, his stamina is not as good as it could be. He definately prefers walks so out of the two I'd pick 1 hour walk, however given the choice I'd incoperate 10-15 mind of fetch in as extra just to knacker him out!

2 questions you ask.........

Better for the dog - I would go for an hour of walking. A whole hour of fetch, too much adrenalin, too much twisting,

Burn off calories -(generally, but it will depend on the dog) fetch, if the dog will do it...BUT - if you were specifically looking to slim down an overweight dog, I would certainly not be playing fetch with them for an hour.
Mine were on the dunes for an hour last night and Gabe, Trip and Siren were pretty much running the whole time, they got more out of that mentally that they would have done playing fetch, and I think they pretty much got the same physical exercise as well.

Daisy`s walks are mostly playing Fetch. If I don`t chuck the ball she goes and mugs innocent passers by to play.