Leaving all the silly childish innuendo aside, I think it probably makes chuff all difference unless you are at the very top of the game where it 'might' have a tiny impact that could be the difference between a 1st or 2nd place in the sprint for the finish line in a race.
For most (and by most I mean 99.9% of the cycling population) it will make no difference, but could hugely affect bike comfort, which will in a roundabout way have an effect on performance. So a 'stiffer' bike may actually have a negative impact.
I say all this assuming we are not including bikes that are so uselessly soggy that the brakes will rub during periods of intense effort (and obviously a set of suitable wheels will be needed too), we aren't including such bikes are we?