Some points I would like to make here are, a less analytical approach should be all thats neccessary on your own system. You've been recording with it for some time and have a feel for how it responds. Record a few songs at the higher rate and the difference should be apparent. Its not the difference between gold and lead but there should be enough of change to realize something has changed.
I wish to clarify another thing. The word length is constant no matter what frequency you record at, its 24 bit. Its just that there are more 24 bit words per second at the higher rate. Kinda like more folds in an accordian.
I believe its really in the mixing stage and addition of plugins where the difference is apparant. I've noticed that if I record one track and one only, I cannot hear the difference between 44 and 96. When math needs to done for mixing and plugs, you can hear the difference. Tracks stand out better. Complex waveforms are produced when you mix more than one track that must be mathamatically summed. Its not happening in the same way as your old analog mixer board, it done with math. So, if you've got to stuff lets say, 5 tracks together (mix, sum) they are all time aligned in increments of 44,100 per second. Each sample must be summed to together, one per each track, in this case 5, to derive a new 24 bit word that is an approximation of that sum action. Five tracks, each recorded at 24 bit must be added together to create one final mix track that represents all five. The more tracks you have, the more compromises the math has to make to resolve them. If you have more samples, 96,000 per second rather than the 44,100, the math becomes more precise in its ability to resolve the complexities of stuffing mulitple 24 bit words into one. Its really about total bit count at 96 k that create more accurate math and less rounding errors.
Looking at this from a purely bandwidth/filter view is only one section of this puzzle. More (in band) data words per second make the math of mixing and plugs more accurate as the complex waveforms generated by mixing are more accurately resolved. Hence, your individual tracks stand out better.
One last point, the complexity of the math of 96 vs 88 is mostly overdone. The machine just works harder, thats all. If the proper formula is applied, the result should be true. Any rounding differences should inaudible.
Bob