We've been round this particular "circle of joy" many times.....including this one where it rapidly descended from a good debate into into a FJ v RW "I'm better than you" load of nonsense.......
http://www.pprune.org/military-aviat...-v-heli-s.html
In sum, a well equipped helo (RWR/Chaff/SPJ/DIRCM/MWS etc) with good SA, excellent crew co-operation and trained in A-A tactics is a difficult target to find, track and kill (both radar and visually) - but this is terrain and weather dependant. A completely unaware, ill-equipped and non-trained helo is still hard to find visually if down at low level but may present a very simple BVR/IR Mx opportunity. For the Helo to "win" it often merely has to survive. Shooting down the FJ is the last thing on your mind, scaring it off, keeping out of its weapon arcs (increasingly hard with HMDCS and off-boresight Mx) until help arrives or running it out of fuel are normally the best options. Re the AH gun, having looked at gun tape of it trying to track me, I'd suggest it's optimised for ground target crossing rates; maybe, at best, a slashing guns shot A-A. The AH can carry Stingers but, with all things, it compromises weight and pylon space - many AH users now put additional podded DAS sensors on the ends of the wings.