At the end of the day there actually wasnt a ton of variation between naval uniforms of the different nations, nor is there to day really.

Here we have Admiral Roze, the commander of the French Far East Squadron and in charge of the attempts to seize parts of Korea. https://upload.wikimedia.org/wikipedia/commons/7/7e/AmiralRoze.jpg

Then we have Admiral Senyavin, one of the more noted Russian Admirals during the Napoleonic Wars. https://en.wikipedia.org/wiki/Dmitry_Senyavin#/media/File:Senyavin.jpg

And Admirals Nakhimov and Kornilov, the Russian Admirals who commanded the defense of Sevastopol in the Crimea https://en.wikipedia.org/wiki/Pavel_Nakhimov#/media/File:Admiral_Nakhimov.jpg https://en.wikipedia.org/wiki/Vladimir_Alexeyevich_Kornilov#/media/File:Karl_Brullov_24.jpg

And finally for comparison Sir Alexander Milne who commanded the North American Station for the RN during the US Civil War: https://en.wikipedia.org/wiki/Sir_Alexander_Milne,1st_Baronet#/media/File:Admiral_Alexander_Milne%281808-1896%29,_by_Walter_William_Ouless.jpg

So as you see they all were remarkably similar. A few practical reasons for that being that officer's uniforms had to be sturdy enough to stand being at sea for long periods of time, and their ability to protect from the elements would be important as well, and the dark colors in part also made the accumulated grime and dirt less noticeable in between laundering. Then the epaulette's are so the officer, and then their rank can be easily distinguished, as a Capt here Perry is wearing one on both shoulders with a star on the shoulder board. Epaulettes were common across all force of the time and indeed in a sense survive today in the more subtle shoulder board. Here is a picture of a Union general just a few year later: https://upload.wikimedia.org/wikipedia/commons/thumb/4/47/CharlesGriffin.jpg/640px-CharlesGriffin.jpg The same goes for the sleeve's even today they are used to tell at a distance the officer's rank in virtually every navy.

It should also be noted that for much of the nation's history while the Army looked to France for new trends and emulation, with good reason, it was not true for the Navy. Even before 1812, and again after the USN and RN established strong working relationships and the US officers took good care to try to emulate the practices of what was at the time the most professional sea service to be found, as did many other nations.