Every single emulator I've ever used has been inaccurate in some way. I don't always care and you may not either; I use plenty of emulators. But I don't consider them a substitute for the real thing; they're more of an added convenience to let me play in different situations than I otherwise could. It's like playing an mp3 on a set of earbuds on your phone vs. playing a song off CD (or vinyl) on a good home stereo.
I usually don't really understand when people make it an either/or thing. I suppose I get that you're having lag issues with the Game Boy Player. I don't really get the lag issues with other consoles over composite or RF, though. That sounds like a TV problem. It's physically impossible for an emulator to have less lag than the console it's emulating, whatever the output. An emulator's added lag may be so slight as to be imperceptible, but it's always adding a layer of interpolation that the original console didn't have to deal with. It can't have *less* lag than the original and still claim to be emulating.
Emulation has gotten better. For example, BSNES/Higan is accurate enough to play all SNES games including those with unusual co-processors with zero bugs. Nestopia Undead Edition is a good NES emulator. For systems that have become too expensive to collect such as Neo Geo and SNES I'll resort to emulation. There is also the convenience factor.
Lag is still an issue and that is why I ultimately prefer the real thing. It just plays better. You're going to have a much more difficult time beating a game like Mike Tyson's Punch-Out on an emulator.
(Note that when it comes to aging console hardware and cartridges and discs that degrade over time, even the real thing is less than perfect and can have glitches that don't happen in emulation.)