Even if you work and export at 16bit/44.1Hz you get different audio then during work.
That's because live works internal at 32bit(like almost all DAW's).
I had always problems with exported audio, never being as same as in Live.
Then I tried to export at 32bit..., and boom...it was perfect !!!
Now I work like that for years, and use only 32bit for all my audio.
The bigger size pays off for me.
Regards sample rate: Work at the sample rate your final product will be.
Audio for CD is: 44.1Hz
Audio for film/DVD: 48Hz
If you need better quality with higher sample rate, then use:
88.2Hz for CD or 96Hz for Film/DVD.
The reason is simple...
When you down convert to the final sample rate, the converter has a even
calculation process, dividing the higher sample rate just by half.
Leaves almost no artifact's...!!!
88.2Hz is double of 44.1Hz or 96Hz is double of 48Hz !
If you down convert from 96Hz to 44.1, you'll get artifacts,
all the time, ...even with the best converter !!!
It can be, that you won't hear it, but technically there are artifact !
There are extra audio information's that won't fit and has to be
down converted with the algorithm.
That's mathematically not easy and leaves audio artifacts.
That's important to keep in mind !
About higher sample rate:
People say they don't hear a difference at 88.2Hz or 96Hz.
I do..., and especially when I use Reverb or Distortion plugins.
They both sound much smoother and warmer !
I have the monitors to hear these differences,
and I took a friend to do a blind A/B difference test with me.
He could also hear it and he's not working with music.
Do a test, don't use just a sample.
Take any vst and add reverb and/or distortion to it.
Export both at small and high sample rate, then listen to them.
Judge yourself...!
greets...