I have used Berkley big game mono as far as I can remember and never had issues with it. The past season I have been using Berkley vanish and I think all it is good at is making your catch vanish! I am only using it for leader material between 5-7ft long for inshore fishing, but I think that is what is causing my break offs. On the boat I switch to big game mono when a fluoro leader breaks off and I can't recall it ever breaking so I think it is the line.
Any recommendations for a good Fluoro leader material? Cost really isn't a factor since you are only using a couple of yards per reel. I actually switched to straight braid on my hard baits and for inshore species they don't seem to care, I can't do that with jigs, the line would get shredded in no time flat.