I would argue it's relative. Some emulators I use on android are every bit as good as pc emulators on the older systems. Otherwise what Sony said is dead on. Emulators that need horsepower are always gonna have an advantage on pc with almost limitless resources compared to mobile units.
As far as bluetooth goes lag depends on the system and drivers. I have used bluetooth gamepads with no lag at all, but bluetooth headsets that have terrible lag. Each machine seems to be different to. My 8bitdo gamepad has worked flawless on damn near everything i use it on for example. However my Bluedio Headphones have terrible lag on almost every android machine i use it on.