Be careful of how you handle this.  My sister have a "pit bull" (they prefer to say Shaffshire Terrior, however you spell it, but to me- both still is same thing).  That dog is one of most friendliest I ever met.  In this town, there's no law against pit bull but a while before that I had asked clerk what animal is forbidden within town limit and she said only pitbull (saying it verbally, never saw it on paper).  I suspect that she is making that one up.  New clerk since then and new law (on paper)- any 'mean' dog will be in trouble, any breed.  What breed most frequently bit people?  According to police, it is black lab since it is one of most popular breed.  We have one!  Yes, in this town NO dog is supposed to be running loose- that may result in a ticket.  The biggest difference is of how pitbull is being treated.  Trained to be a fighter?  Treated harshly?  Treated as loved family pet?  ANY dog can be mean, very mean.  There's one dog in this town I do NOT want to meet (I found him while delivering newspaper) and he is not a pitbull, he is doberman.  This dog was kept in garage, never loose outside on his own.  My little girl has been attacked by two different dogs.  Austrilian shepard and St. Benards.  Very thankful that it is not any worse!! and that she is not afraid of most of dogs.  Be careful of how you imply that it is that pitbull that attacked your dog last December.  What about racoon?  One can put up a good fight.  What about old tough wild tomcat?  Ouch.  How about try to get to know that neighbor better?  Try to get on friendly terms with them at least to the point of being able to call them nicely to inform them that their dog is on the loose.  If you are that concerned, then why not consider putting up your own fence?  Out on a walk?  Take a walking stick.  Is it possible that that pitbull is so lonely that all he could do is watch you all?  Are you sure he is only barking in his own rough deep rumbling way, not being mean at all?  Have you ever thought of trying to make a friend with that dog?  Leave doggie treats on his side of fence at regular time.  Maybe you'll be surprised.  Shuiti dog across the street sometimes slipped away.  He once came over and refuses to go back home on command and couldn't be caught, so I gave him a whack on his nose with a nose by surprise with a long stick.  I haven't seen him back over here since.  I'm not afraid to use powerful air rifle on any unwelcome critters around here.  It is not legal to fire any firearms within townlimit but multiplying rabbits can cause chaos in my gardens.  When I first moved here, I often see loose dogs.  But after pet license are required, I see very few.  Please do try "loving your neighbor" first.  Of course if neighbor fail to "love you back" then I'd quietly take pictures and call police every time you see that dog on the loose.  Dog pound too if police isn't much help.  Safety of your children comes first especially when others refuses to cooperate.

Just my opinions...

I think I understand what you meant.  I too was a bit concerned until I met my sister's pitbull.  Media does influence of how you look at things.  Try to think about the value of making friends with that dog so you could safely guide him back to where he is supposed to be especially if owners aren't home- even tying him up in your yard or put in your own kennel until owner comes home.  Just so that dog isn't running loose anymore.  Do to them as you would want them to do to you.  I don't report loose dogs because I have no proof as to who it belongs to and usually they are gone before I could return with a camera.  Should I get tranqulizer gun?  But then I do not want to mess with determining the dose so I won't accidentally kill it.  Is your dog running loose? then consider hard of how to keep him home.  Leash of any kind.  Kennel.  We use kennel for our dog, never used chain.  That kennel is escape-artist-proof (this took several repairs and modifications).  Teach and train your children to respect ANY animals especially those that don't live with them.

It would be interesting to personally hear what police think about dog attack/biting.  Same goes for vets, groomer, and kennels.

I think I know the difference between attack and biting.  No difference to a mother of injuried child!  First one was definately an attack- I personally saw it.  If I already have a rifle in my hand then, that dog would have been immediately dead.  This was on their property!  He was later was disposed by that family since dog became too aggressive towards his own children.  Second one, no proof but highly suspected that dog only snapped at her and her hand was in the way.  Nobody saw this happened.  I had Pinky show me which animal that 'bit' her (this was on a farm).  That dog never became aggressive with anybody since.  Think two year old treating other dogs the same way as our own without any regards.  Ouch.  These was during the months of me trying to train my daughter NOT to "squeeze" (with hands only, not at all like a hugging kind)  nor to pull on ears/tail.  Pinky improved tremedeously since then!

While on loose dog subject- I would shoot any dog caught chasing a deer.  DNR man gave this advice.  Keep your mouth shut and bury the dog.  That way, you won't troubled by and/or get sued by dog owner.  That dog would simply dispappear without a trace.

You think Springer is best dog for children.  Others think not. Okay.  I can see similar parelle with pitbull but I'm not sure how to put it down in words.