Well, if we compare a final export in 44.1 vs 48, I don’t think there will be much difference, if any.
When talking about 44.1 vs 48, it isn’t really a “better quality” question, but more like “how not to lose quality”.
This is more related to the mixing process in the DAW itself than to playback on an end device.
I’d recommend to work in 48 kHz instead of 44.1 whenever it is possible :
Most audio interfaces record frequencies up to 20 kHz, but if we look at the Nyquist frequency, which is half the sampling rate, we can see that it is very close to the highest recorded frequency – 22 kHz in the case we’re using a sample rate of 44.1.
When we further process the audio with effects like saturation and distortion, the created harmonics that go beyond the Nyquist frequency will bounce back and produce aliasing. It can become more or less audible depending on how loud the frequencies that go beyond Nyquist’s are.
So, in the case of a 44.1 sample rate, there is only 2 kHz of headroom, while with a 48 kHz sample rate, there is 4 kHz. This may still not look very much, but these 2 more kHz of headroom will strongly reduce the effects of aliasing, and the increase in CPU ressources and file size is completely negligible here.
Most plugins now have internal oversampling capabilities which eliminates the problem, but if for any reason you are using plugins that do not feature it, then it is good to have as much headroom as possible to start with.
Some audio interfaces can record up to 35 kHz when they are set to 88.2 or 96 kHz sample rate, which then effectively increases the quality of the recordings, since it captures more of your microphones and instruments, with the Nyquist ceiling being much higher at the same time, but at the cost of twice the CPU usage and file size.
However, if the recordings are done with an interface that can only record 20 kHz, then there is no need to set the sample rate to 96 kHz and you can stick to 48, as the plugins will already oversample the signal before processing it.
There are very nice videos that dive into the details even more :