Would upgrading my computer's Bluetooth improve the audio quality?
Bluetooth 4.0 should improve audio quality, provided you have devices that support aptX or A2DP:
Does Bluetooth Audio Still Suck?
The problem with Bluetooth audio has always been digital compression:
in order to send your audio to your headphones, you were forced to
sacrifice quality. Traditionally, especially on older devices and with
older Bluetooth versions, this meant the sound was so badly compressed
that the result sounded robotic, buzzy, noisy, and all around awful.
Listening to podcasts and spoken word through them wasn't a big deal,
but when it came to music, they were just the worst. You got none of
the richness or warmth of sound that a pair of wired headphones
offers.
In addition to compression just ruining the audio quality, there are
other factors at play. For one, Bluetooth rides the same 2.4Ghz
wireless frequency that so many other things in your home, like
wireless mice or keyboards, Wi-Fi signals, or even microwaves.
Those things won't have a huge impact on sound quality, but they
can—and often do—cause audio drops and other quirks. Of course, all of
those are reasons why Bluetooth audio was never—and still isn't—a
match for traditional wired audio. That doesn't mean it's without its
merits.
...
Bluetooth has improved, and the audio compression isn't nearly as bad
as it was even five years ago. Bluetooth standards have improved
significantly since the days of Bluetooth 1.1 and 2.0 (which is when
Bluetooth headsets and headphones really hit the market), and today's
Bluetooth 3.0 and 4.0 devices are built with more attention to stereo
audio in mind.
If you want the best possible audio quality from a Bluetooth device,
look for headphones and speakers that support aptX, an audio codec
designed for CD-quality audio transfer over Bluetooth. Alternatively,
look for support for A2DP, or Advanced Audio Distribution Profile,
which also requires compatible devices, but is designed for sending
stereo audio over Bluetooth to speakers, car stereos, and headphones.
In either case, even if you don't have supported devices, you may be
able to find adapters to help bridge the gap.
That said, it's still not as good as wired audio, and some people say
it's still unacceptable overall. Still, there are situations where
it's good enough for what you want.
Source Does Bluetooth Audio Still Suck?