We are not saying that the higher bit depths are not better than 16 bits/44.1kHz. What we are saying is that the end product will be a 16 bit wav/aiff file if you are burning to CD or using the file in some other program that does not necessarily share the same file format as the 24 bit or 32 bit floating point (flpt) representations that your daw may use..
As you may have got from the discussion between myself and d'ranged, higher bit depths do result in more subtleties in the represented sound (24 bits will give you 256 points of difference for each point in a 16 bit bit-depth; i.e. the sound can be represented 256 x more accurately), this is why the file sizes for comparable files at different bit depths will be markedly different: 24 bit is larger than 16 bit and 32 bit flpt is larger than 24 bit.
In other words, the bit depth does not necessarily translate to different software in the way that we would like it to.
Secondly, once you create something in camtasia or any other movie editing program, the output file may not necessarily be able to cope with higher bit depths or even a 16 bit bit depth. Check what the output file claims to be: what bit depth and codec for the video, frame-rate, and most importantly the audio bit depth and codec.
This is where your quality issues will start to bite.
It may also be that your initial mixes are less than
stellar, leading to quality issues that you aren't aware of before you even start to edit it to video or
vice versa