Dogs are one of the absolute worst chicken killers. We can't tell you if your neighbors dogs in particular will kill them, but most dogs that haven't been taught to leave them alone will ...and often once a dog learns the fun of chewing them up they often return for more fun if they can.
Brandon - you must be really new to chickens or haven't read this section of the Forum at all. Dogs are always a threat. I'd say almost half of the predator complaints reported here involve canines, either neighbors, our own, or strays , or the wild types like wolves and coyotes. Those of us who free range accept the risk, after doing what we can to minimize the risks with fences and guardian animals.
Not all dogs are threats, but it's near impossible to know which ones are.
It's never a great idea to take risks when your chooks are involved.
Heck, our next door neighbours dog could've easily clear our fence and did at one point, found her lying down in our back garden with our chooks happily pottering around. Some dogs mean no harm, and sometimes even the gentlest of dogs can snap if there's cause to.
Some dogs are chicken killing machines. Some dogs wouldn't hurt a chick. There is really no reliable way to know which dog is which until you expose it to chickens.
Except for dogs bred to control vermin like a feist, Dachshund, Sheba enu, Jack Russel, and other terrier breeds (dogs of the Earth) whose sole purpose is to run to earth, corner, and/or dig out any thing that flees from them and kill it at all hazards, the breed of dog is a poor predictor of how it will behave with chickens.
I have a well fenced yard as people tend to just let their dogs run free around here. I assume any dog is a chicken killer to be safe.
My own dog is a Malinos, he loves the chase of a chicken but once he stands over it, he's done. He will pin it, but will not bite or kill it. He'll stand between (I've caught him doing it) my hens and predators, even standing over the chicken and staring the predator down. My friend's terrier mutt, is a chicken herder and gathers up flocks to be put away but never does anything beyond chase. Her other dog she was sitting though, was a mass chicken murderer. So you have a large range, therefor you can never tell.
Good fences make good neighbors. So long as the dogs never get into the yard, they will be fine. Dogs can dig into pens too, if they are dirt/ground, so I always secure mine in their elevated coop at night so that even if something did get in, it would get my precious chickens! During the day though, they have fenced pastures to roam in and a dog that knows better now than to chase.
Dogs can and will kill chicks. Learned the hard way as my own dog killed my first three chicks. Dogs can also be great protectors of your chickens. Same dog now leaves my chickens alone but will chase any other bird or predator off property including hawks, pigeons and raccoons.
Dogs are one of our worst predators. In this case, a stout fence with a hot wire run along the bottom or wire mesh along the bottom to prevent digging may be your only option.
We use the shotgun method of dog control--but these are your neighbors....
That being said, we trained our dog (Pit Bull/Mastiff cross) to leave the hens alone. Just yesterday I watched as a broody hen led her chicks next to and underneath the dog to reach the compost pile. But it's very hard to train your neighbors' dogs.