Given your answer then you should definitely be using equation_html

The difference is really in terms of what is return from the editor.

With version 1 (equation), you get back pure latex, i.e.

\[\frac{1-\sin(x^2)}{x}\]

with version 2 (equation_html), you get back html for the equation, i.e.

<img src="http://latex.codecogs.com/gif.latex?\frac{1-\sin(x^2)}{x}" alt="\frac{1-\sin(x^2)}{x}" />

As such with version 1, we run a 2nd step afterwards to convert the latex to html on the fly. If your creating a lot of equations and often like to write them without using the editor, then version 1 can be easier to use. In almost all other circumstances you're better off with version 2.

Hope this helps explain the difference.