There are now emulators for the SNES that have 100% accuracy.
Emulators typically take shortcuts in order to speed up the emulation, but we are at the point now where CPUs are powerful enough to have accurate emulation of the SNES without needing to use them.
This means that you can now emulate a SNES and sound will be exactly the same as the real hardware now (a lot of older emulators sound really bad when you compare them to the real hardware) and you no longer have the limitation of a 480i RGB output at best - you can output to your display's native resolution with pixel-perfect accuracy.
If you are trying to play on a flat panel, this can make a considerable difference, as most flat panels do a terrible job of handling interlaced inputs - especially from games consoles - and upscaling from 480i typically adds a lot of lag. (and you already have a minimum of 1-2 frames of lag if you are using a flat panel) I've spent a lot of time with devices like the XRGB scaler family to try and get decent results on flat panels and while they work OK, they still don't look nearly as good as emulation.
You also have the advantage of trying to emulate a CRT if that's your thing. While I don't like a lot of the "NTSC" style filters that emulate a crappy CRT connected up via composite, or "scanline" filters that simply add black/gray lines over the image, there are some which soften the look of the hard-edged pixel graphics in a more natural way, and help make dither appear as if it's a transparent color as originally intended.
The problem with this emulation though, is that to perform with 100% accuracy, it means emulating the clock speeds perfectly, which has given me trouble. Due to how PC architecture works, audio and video run off different clocks, and video cards are a bit loose with their timings, because monitors don't need exact refresh rates to sync correctly (they are usually quite tolerant) and the emulator itself has no control over the video card clocks. On the other hand, NTSC is exactly 60/1.001Hz, and the SNES itself did not conform to NTSC standards exactly with its output. From doing a quick search it seems that it was either 60.08Hz or 59.97Hz depending on the output mode. (NTSC is around 59.94Hz)
This means that I have never been able to get perfectly smooth gameplay with these emulators and have to put up with either: stuttering, audio distortion, audio sync issues, or screen tearing. (v-sync issues)
It seems like this would actually be a relatively simple fix if the emulator dynamically changed the SNES clock from 59.97/60.08Hz to whatever the video card clock is outputting, resampling the audio to match, but then you don't have "100% accurate" emulation. (even though it would be a much better experience)
That's a problem you never have to deal with if you are playing on the original hardware - though you may have other problems caused by things like improper cadence detection if you are trying to play on a flat panel. (resolution pumping, combing artefacts, stutter etc.)
If you can source a good CRT (the Sony BVM or PVM monitors are often available second-hand these days, and are amazing) and a working SNES with an RGB cable, I would say that's still the best option to use today.
If not, you are probably best with emulation - especially if you don't care about 100% accuracy, because then you shouldn't have any audio/video sync issues. (they only appear when you are doing accurate emulation in my experience)