Am I in the wrong or can my neighbors take action

IMHO, most of what is going on here is more issues of managing relations with your neighbors that may require practical rather than legal solutions, but there certainly are legal risks.  First, there will be some sort of city or county local ordinances on barking or nuisance dogs and/or noise ordinances, and you should familiarize yourself with them as neighbors may well make complaints to Animal Control or Code Enforcement, and there is a always the risk they could consult a civil attorney as to civil nuisance claims.  If you are renting, complaints to your landlord can easily result in the landlord deciding not to renew the lease and potentially in the landlord taking action prior to the expiration of the lease.  Finally, if you have neighbors who hate your dogs, you need to beware that if they accidentally get out, you are almost certainly going to be reported for the violation.  On the practical side of things, while you may know from the dogs conduct inside the house the dogs true temperament, all your neighbors know is that the the large dogs are of breeds that most people feel are dangerous and exhibit what the neighbors perceive as aggessive barking when both are in the back yard at the same time together.  As a practical matter, unless you are watching the dogs in the yard all the time, you have no first hand knowledge what is going on back there and if your response to neighbor's concerns is that they are lying, when they could be telling the truth, this is making things worse and not better.  If you are leaving the dogs outside for hours when you are not at home, it is always possible they are barking for longer periods.  No matter what the issue, it is always a bad thing to be involved in a hostile situation with your neighbors and it is well worth going the extra mile to keep things "neighborly" in the long run.  Possible solutions involve introducing neighbors to the dogs in a neutral situation, asking them nicely to go outside at a time when you can observe the dogs and what they are doing, even putting cameras in the yard so you can monitor dogs behavior, and finally making sure your fence is absolutely secure and there is no possibility the dogs can jump the fence.  Finally, as the owner of several Pitty/Staffy mixed breed rescue dogs, I know how sweet their natural temperaments are, but they have a terrible reputation, IMHO mostly resulting from by cruel and neglectful owners who mistreat and abandon them and/or good hearted but inexperienced folks who fail to appropriately train and socialize them with other dogs.  Good owners can be breed ambassadors by making all interactions with their dogs an opportunity for folks to see their true colors and sweet natures.  Best of luck.