Fallout 3 main music with custom made video for the main menu, they should fit well together, give it a try!
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I just made a custom Fallout 3 video for the main menu, and mixed a bit the Fallout 3 music, with reverb and level adjustments, also made the second part ( from when the heavy drumming starts) more impactful, I find the original a bit flat. It also fits well the video because of the reverb ( which makes the music more as it sounds outdoor, not in a recording studio as the original) and effects ( to make the sound more raw, which better pairs with the Fallout 3 video style) and levels adjustments (to emphasize certain moments, like for example the heavy drumming in the second half, to give an "increasing" feel to it, in the original all the song has the same volume, from start to end ). Not big changes overall, anyway ....
TO INSTALL, just put the "Data" folder in the Fallout 4 main directory, and don't forget to backup your original video in the game, simply rename the "MainMenuLoop.bk2" file in your Fallout 4/Data/Video folder to "MainMenuLoop.bk2xx" so it will remain there in case you want to revert it to the original Fallout 4 menu video. No needed for the audio file, just delete it.