There is a gate to the neighbors yard? I would remove that to prevent this happening again. There is so much breed discrimination that I believe you are correct that it would be a losing battle. Bulldogs used to be the All American Dog 100 years ago. At the shelter where I worked we got little terriers all the time that were surrendered for behavior. Just about all of them were pretty bad dogs. Any dog with miniature in the name is trouble. On the other hand most of the Pit Bulls were fine. If your neighbors dog torments your new dog I would address that proactively. Complain to animal control every chance you get a videotape it. Then you will have something to show the jury if anything ever happens like the little POS crawls under the fence or something. IMHO. I am very sorry for your loss.

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1998 C230 330,000 miles (currently dead of second failed EIS, yours will fail too, turning you into the dealer's personal human cash machine)
1988 F150 144,000 miles (leaks all the colors of the rainbow)
Previous stars: 1981 Brava 210,000 miles, 1978 128 150,000 miles, 1977 B200 Van 175,000 miles, 1972 Vega (great, if rusty, car), 1972 Celica, 1986.5 Supra