Looks like an american bulldog cross, maybe a bit of staffy in there.
Have you spoken to your neighbours about sorting the fence out?
If you have concerns about the dogs behaviour or welfare you'll need to try the RSPCA I think.
There are no such thing as 'safe/good' breeds and 'dangerous/bad' breeds. However of course different breeds of dog ARE different in their strengths, temperaments and behaviours and do require different handling, that needs to be recognised and catered for properly.