Q: When integrating local additions, is there a reason to prefer one approach over the other?
I'm guessing that TEXINPUTS is just regarded as the quick and dirty approach while registering a local texmf tree may be a better idea if you have a lot of files within a logical directory structure to which latex needs to be pointed.
If I'm missing something here I'd love to hear about it :)
TeX itself uses TEXINPUTS and it can cause an error if it is also set by the user. An almost secure way is to use a local texmf tree. With MiKTeX you can have several of them. For Linux you have TEXMF, TEXMFLOCAL and TEXMFHOME. The latter do not need a `texhash´ command, it is searched recursively by TeX.
TEXINPUTS is easier and works best for ad-hoc files. If you use the same files with different jobs, and particularly if you have other kinds of files such as fonts, you are best off using a Texmf tree because you do not need to manage environment variables and the Texlive command-line tools understand the Texmf tree better.