0 opacity: object still renders itself to the screen processing any effects, taking the GPU's time, but most likely results in nothing being changed on-screen. However, if you had an effect which did something like invert the opacity, it would still be seen.
Invisible: object skips drawing at all so will never be seen under any circumstances. Therefore GPU spends no time at all trying to draw the object.
In short, use 'invisible' instead of 0 opacity to hide objects, it's faster.