SameOrDifferent -- Watch on the Moon vs Watch to the Moon: indeed it sounds so close, but maybe there are differences between the OnTheMoonWatch and the ToTheMoonWatch -- the first is quite well known, sells for USD25'000 or more and was made by Omega. The second is not so popular, much cheaper and made by Bulova.

When Edwin E. Aldrin set his feet on the moon-surface approx 20 minutes after Neil Armstrong (who didnt wear a watch; so the importance of the MoonWatch at all, could be discussed in this light;), he was wearing an Omega Speedmaster: the Omega (OnThe-)MoonWatch. Nothing really revolutionary but a reliable, solid and robust mechanical watch that passed the NASA-tests with bravour (and eventually financed a portion of the expedition?). However, neither Neil Armstrong nor Edwin Aldrin nor the Omega worn by the number two Astronaut on the Moon could have been there without a more revolutionary and much more precise watch: the Bulova Accutron, the ToTheMoonWatch. Indeed, the first electronic watch that increased precision by magnitudes and came in their most characteristic version without a dial, named SpaceView.

So in the direct comparisson we see the more relevant watch in this story is electric while it was perfectly fine to run a mechanical watch on the moon. It was 360Hz vs 3Hz; time-only vs Chronograph; <30 parts with 10 moving vs approx 300 parts most of them moving; 180m of copper-wire with a diameter of <0.015mm (!sic) vs nothing comparable;