Those are very different commands even if the output happens to look the same.
If you want to emphasize a word or some text, use \emph. Don't just make the text italic or bold. If needed, you may change the behaviour of \emph whenever you wish in the preamble and the whole document will be adjusted accordingly.
If you want to get italic text, use \textit. \emph might have a different effect, a package like ulem might change it to underlining for instance.
\emph may be nested: emphasized text within emphasized text may be upright. In contrary, nesting \textit just keeps the italic shape.
Further, I rarely use physical font commands in my body text. I use them to define styles in the preamble and use the styles in the document afterwards, ensuring consistency and allowing changes to be easily made.