The main advantage is better signal to noise ratio and secondarily, better frequency response (because the groove wiggles are stretched over a longer length of groove.)
I'll also add "better dynamic range"...those 12" 45 RPM records were simply awesome compared to regular LP sound. I used to buy tons of them (about half my old collection). The most noticeable improvement was in the bass. Less feedback issues especially at higher SPL levels. I am not sure if many night clubs still use them today, but these used to be the pro's choice to blast out quality hits over high end club systems and draw crowds. (A quality of sound production that few could match at home)