As far as I know,
There are pros and cons.
I'm not a specialist or scientist but have been internated in technical things about sampling rate so I searched and read articles, forums, books.
I think Aliasing, EQ, IMD and SRC, are the important things.
For aliasing,
compressor, limiter, distortion, saturation and these kinds of process usually produce upper frequency information, and this could go above nyquist frequency, which will result aliasing noise. So, technically, with higher sampling rate, there will be less aliasing noise when you are mixing or mastering because nyquist frequency is set higher.
Also, when you tweak EQ near the nyquist frequency, the EQ curve doesn't be like you'd expect. It acts differently when it gets close to the nyquist frequency. (in a bad way i think)
So if you think about these, higher sampling rate like 96khz can be better.
Some plugins internally process at doubled of multipled sampling rate (oversampling) to avoid aliasing or that. The higher sampling rate is better in some case.
However, whenever you use non-linear processes like I mentioned above (compressor, distortion, etc.), they also produce IMD.
If the original material or recorded track has
a lot of information that we can't hear, lile above 20khz, these unnecessary information produces more IMD. So this is a downside. To avoid this, you can use a filter to cut these frequency before you put non-linear process.
So with higher sampling rate with unnecessary information, you might get even worse result because of IMD. I read this thing on gearslutz forum.
For SRC, I think you eventually release your songs at 44khz, so if you produce your music at other sampling rate, you need to convert the sampling rate with SRC. You can use SRC on your DAW but the quality of SRC is different on each program. And whenever you use SRC, the sound get worse and peak changes. (only just slightly and no one might notice though) anyway, usually SRC in your DAW is not ideal, so if you don't have decent SRC, the track converted to 44khz may sound worse than one with 96khz. IFAIK SRC on ableton live is great among DAW. SRC by Saracon or izotope are considered to be best I think. You can check the quality of SRC on SRC comparison website.
Reverb or other process may act differently on different sampling rate but I just don't know it.
Intersampling peak at higher sampling rate is beyond this topic I think, too.
So the end result will be really different not because you record it on higher sampling rate but you processd it on higher sampling rate.
I currently master at 96khz with ultrasonic filter to lessen IMD but for other thing like mixing or producing. I don't know which is better because higher sampling rate seems to require more CPU.
So, for producing, mixing mastering, there will be some difference in sound. But for recording, there might be subtle differences technically but these might not be significant.
If you mix at higher sampling rate you can record them at higher sampling rate to avoid unnecessary process.