Existence of atoms - Einstein or Smoluchowski

Einstein was first but also much more popular. Smoluchowski's work appeared one year later, give or take, which I suppose is not a long time considering the speed of information flow in 1900. His result also was off by a little with respect to Einstein's and, in my opinion, while more elegant from a physical point of view also a bit more cumbersome.

But I would argue that Einstein's preminence is mostly due to general popularity.

His 1905 work on Brownian motion is part of his Annus mirabilis series which contributed to making him the "model" of a genius we now consider him to be.

Also, Einstein's theory was initially proved wrong by initial experiments by Svedberg, meaning that no clear solution of the problem was reached before 1908-1909, so Smoluchowski's theory also had been long around.

An even brighter example that this has to do with popularity rather than novelty is that another often forgotten name is that of Jean Perrin who won the 1926 Nobel prize for his experimental realization of Einstein's theory in 1909.

Both he and Smoluchowski, today mostly unknown if not by specialists, are victims of Einstein's popularity. But they were praised during their times! Smoluchowski and Perrin (and others) are now often credited too, but people mostly remember Einstein.