(Modern usage of the word Sophism) "The essential claim of sophistry is that the actual logical validity of an argument is irrelevant (if not non-existent); it is only the ruling of the audience which ultimately determines whether a conclusion is considered "true" or not. By appealing to the prejudices and emotions of the judges, one can garner favorable treatment for one's side of the argument and cause a factually false position to be ruled true." Wikipedia
"Nihilism is a philosophical position which argues that the world, especially past and current human existence, is without objective meaning, purpose, comprehensible truth, or essential value. Nihilists generally assert some or all of the following: there is no reasonable proof of the existence of a higher ruler or creator, a "true morality" is unknown, and secular ethics are impossible; therefore, life has no truth, and no action is known to be preferable to any other." Wikipedia
So you can see that any argument made by either a Sophist or a Nihilist would be very similar. Regardless of the facts in a given argument, a Sophist (modern usage of the word) would argue that the facts are irrelevant, a Nihilist would argue that the facts are not knowable. Both disciplines have little regard for "truth."