Bit-perfect is a phrase commonly used in the audio world. When used to describe a media player, it means the player can output an exact copy of a file without making any changes.
Some players don't do bit-perfect output. This might be because they output through the system mixer which resamples to a common "mixing sample rate" (iTunes, WMP, etc.). Or it might be because they don't support the output method necessary for certain hardware to work well (Winamp, etc.).
However, many good players can do bit-perfect output, JRiver Media Center included.
A good starting point when picking an audio player is to make sure it's capable of bit-perfect output.
Bit-perfect output is just one of many, many features of a media player. Also consider performance, stability, format support, user interface, remote support, device support, etc. All of these things work together to help you enjoy your media.
Bit-perfect vs Bit-processed
Roughly speaking, people think about digital audio in one of three ways:
A) The source is perfect, and all processing is bad processing
B) Good sound is the goal, and sometimes processing can help
C) Processing can be good, but I want to do it in my external hardware
If you're A, all you want is bit-perfect output. Many players do this, JRiver included. They all sound the same. Pick the player that checks the other boxes listed above (performance, user interface, etc.).
If you're B, JRiver has an unparalleled audio processing engine – simple things like 64-bit volume, all the way to complicated things like unlimited parametric processing, Room Correction, Convolution, ISO 226:2003 corrected volume, etc. A computer is an amazing tool for audio processing with nearly unlimited performance, flexibility, and audio quality.
If you're C, you might consider moving towards B. Computers are awesome. They don't have the same pretty lights as your expensive hardware, but they can decode and process audio in a way that will deliver the highest possible quality.
Sound of Bit-perfect
Bit-perfect players, playing the same content, running in bit-perfect mode sound the same.
This is the definition of bit-perfect. Computers are deterministic.
The only relevant things happening for audio playback are:
1) Delivering the right bits
2) Delivering the bits fast enough
3) Keeping system usage low enough to avoid trouble [this is debatable]
Lots of players do number 1, and it's easy to measure.
Number 2 doesn't affect sound quality unless there's a shortfall, but regardless, JRiver Media Center has the most efficient buffer fill that can be implemented on a computer (a no-lock circle buffer with no additional processing). In other words, there's no room for improvement here.
Number 3 is slippery and debatable. It doesn't make sense and can't be detected or measured when using good audio hardware. And if there is a problem, it's obvious (ticks, hiccups, hum, etc.) and not something subtle with regards to clarity, soundstage, etc. Regardless, JRiver Media Center uses less than 1% of a modern CPU for normal playback. It is elegantly multi-threaded. No player is more efficient.
If someone is trying to sell you a product that has a “better bit-perfect”, they're tricking you (and maybe themselves).