Dealing with non-English sorting
The BibTeX program was written primarily to deal with references in English. It is very limited in handling accented characters, and even more limited with non-Latin letters. In contrast, the Biber program was written from the start to handle a mix of scripts properly.
This means that if you are sorting your bibliography, and you need to sort in anything other than English order, you really should be using biblatex and Biber, rather than natbib and BibTeX.
Hyperlinks
If you load the hyperref package (as covered earlier), it will automatically make some content in your bibliography into links. This is particularly useful for URLs and DOIs.
Differences in best practice for BibTeX input between styles
While the overall syntax of the BibTeX files is the same whether you use the BibTeX workflow or biblatex, the set of fields that is supported (used by the style) and their exact meaning may not only vary between the BibTeX workflow and biblatex, but also between different BibTeX styles. A large ‘core set’ of entry types and fields is the same for almost all styles, but there are differences in some fields.
A common example is the URL. Some older BibTeX .bst styles (most notably the ‘standard BibTeX styles’, e.g. plain.bst, unsrt.bst, …) predate the invention of the URL and have no dedicated field for the URL of an online resource. Many newer styles do have a dedicated url field. The workaround to show the URL in the older styles is usually to use the howpublished field, but with the newer styles it is of course preferable to use the dedicated url field.
In order to be able to make use of the full potential of your used style you will have to find out the set of fields it supports and their semantic.