I can help:
I am betting they’d make you a play thing and kill you.
There might be a little hesitation at first but the predator in them is always forefront.
Indeed, cats are blamed for being colossal murdery bastards when it comes to wildlife. Sweet kitty that cuddles you will happily murder all the animal life it can get its paws on. Something a domesticated dog rarely does.
In the United States alone, cats kill an average of over 2 billion birds and 12 billion mammals each year. Cats are the leading cause of non-natural bird deaths, accounting for just under 75 percent, according to a 2015 study. SOURCE
I think that’s lack of ability more than lack of will. Every dog I’ve known has been more than happy to run at a squirrel if given the option, they just suck at closing the deal.
My murdercats have a nice fenced patio through which they may eck-eck-eck at birdies. Any bird, bat, squirrel, mouse, vole, snake, spider, or dragonfly that chooses to enter the catio does so at its own risk.
I’ve seen cat’s around pet birds and mice without the urge to kill them.
I’m not sure the dog would kill the squirrel once caught. Certainly a prey drive is being triggered here but if they could close the deal would they? I kinda think that if they ever got the squirrel they’d kinda be confused as what to do next. Fido was never raised to hunt food so, while the chase squirrel part is there, the what to do with squirrel once you catch it is not. Squirrel is not food to them. Of course, some rough handling during chase and catching could certainly injure or kill the squirrel.
I remember my dog going after a rabbit once. It was in a huge park. She took off like a bolt and that rabbit was going flat out. I was chasing them and calling my dog to stop. Needless to say my chasing and waving my arms and yelling at my dog was comedic and wholly ineffective. Fortunately the rabbit escaped into a hedge my dog could not get through.
That falls under “sucking at closing the deal”. The prey drive is there as a predator but they lack the skill in following through. I’ve had cats that never really learned to hunt due to being removed from their mother and fellow kittens at a young age. They’d corner a mouse but then just mew plaintively in confusion at what to do next.
Edit: For what it’s worth, I do think/agree that cats retain more of an instinct for hunting & killing, but just don’t think dogs are immune to it’s allure. We just don’t see them killing umpteen bajillion small animals a year because they’re not very skilled at it and are pack animals so solo hunting small critters probably isn’t their forte either. I suppose the flip side of that is your “ratting” dogs, terriers and whatnot designed to kill vermin, but that goes back to “They’re happy to do it if the option is there”.
Goodness. I’ve witnessed several domestic dogs killing other dogs, cats, and squirrels.
Yes, cats are both cuddly and murderous. In fact, here’s my kitty, Mr. Whiskers, about to take down another apex predator:
That whale has no chance. 
I have an indoor cat so I rarely have problems with squirrels. He doesn’t bark, is self cleaning, easy to feed, and the litter box is much easier than the land mines left by dogs. He’s trained in formation napping with me on the weekends. I can exercise him with a laser beam on the wall.
I think it is a matter of degree. Certainly dogs kill things (including humans on occasion; something I think cats almost never do (queue someone showing the one time a domestic cat killed a human)).
But cats are a much, much, much bigger scourge to small animals in the environment than dogs are.
No disagreement from me.
Ask a sheep farmer about that sometime.
And every farm dog I’ve ever known, including the ones properly trained not to hunt sheep, chickens, cats, etc., successfully hunts mice, woodchuck, and rabbit; and tries to hunt squirrels.
Some individual dogs have little or no tendency to hunt. Some individual cats don’t, either. In dogs this is likely to be related to what breed they are; but domestic shorthair cats, at any rate, are all over the map.
Mine did. Caught one on the ground once, killed it with no hesitation.
I’m puzzled by the impression you have that dogs in general aren’t hunters. Have you only known dogs of a few breeds? and/or dogs that never got the chance to learn how to hunt?
Have I mentioned my acquaintance with a domestic cat and dog? There may be a bird involved as well.
I recently sustained a laceration from a fall. From the moment I fell to the time I left for the E.R. 10 hours later (long story), my cat stayed by my right side (where the injury was) and purred. She understood that I needed help, and she understood that the only way she could help me was to stay by my side and purr. And it was a big help. A dog would have stayed by my side, but would not have purred.
And hours later, when I returned from the E.R., she was waiting for me at the door.
This is the same cat who has taken down mice, in spite of having been de-clawed.
We are painting with a broad brush in this thread. Necessarily so when talking about all dogs versus all cats.
You can certainly find edge cases. I’d say dogs owned by sheep farmers is a much smaller set than all domestic dogs. Dogs used to do a job are going to be far more rare and far off the “usual” behavior than most domestic pet dogs.
Gotta love them though. I loved watching dogs used to herd sheep and the farmers played pong with the sheep (the dogs would move the sheep according to commands as two farmers tried to score goals with the sheep). Totally fantastic but waaaay out of the common experience of most pet owners.
Dogs owned by sheep farmers very rarely hunt sheep. It’s other people’s dogs who hunt sheep.
Where did I say they hunted sheep?
Why would a sheep farmer have a dog that killed their sheep?
You didn’t, and they wouldn’t.
You responded, or I thought you did, to my ‘ask a sheep farmer about that’ as if you thought I was talking about the sheep farmer’s dog. I can see why, because in the next paragraph I was indeed talking about farmers’ dogs killing animals of other species; but what I meant by that was that sheep farmers worry about protecting their sheep against other people’s dogs, because dogs who aren’t trained not to hunt sheep most certainly do so. Not dogs of all breeds, of course – the tiny ones can’t, and some of the large breeds have had killing instincts bred out of them over many generations. But very many dogs will kill sheep if not trained otherwise and if they get the chance.
ETA: I’ll also add in here that cats can be raised with rabbits, rats, etc. as household members; and those cats will not kill those rabbits, rats, etc.; just as most dogs raised with cats as members of their household won’t kill those cats. So I’m very dubious about the theory somebody raised in this thread that the only reason cats don’t kill and eat their humans is that the humans are bigger than the cats.