It all depends on what you mean by the best. To me, Japanese cars are better than American cars. All car companies will have cars that break down and aren't perfect, but American cars of late break down so much more than Japanese cars, mostly because they're made with such old and crappy technology down in Mexico, but meanwhile most Japanese cars are made with newer technology in America, Canada, and Japan.
Though the biggest thing to me as to why Japanese cars are better are the following:
1) They can get more power out of an engine than American manufacturers can.
2) They can make a car that corners.
3) They can make a car that brakes so much better.
4) Their fuel economy sucks.
Look at the new Corvette. Most of it is made out of ABS plastic that deforms quite easily, it can't corner for sh*t without a hell of a lot of mods due to it's prehistoric rear end, and it weighs a ton. They need a 7L, 427 cu. in V8 to get 505HP out of the 2012 Z06. Meanwhile, the Honda HSV-010 (which is going into production soon) makes 485HP from it's 207.3 cu in V8. Less than half the capacity as Corvette's engine and nearly the same horse power and is only going to be selling for about $20,000 more than the newer Corvette.
In America, it's all about displacement, displacement, displacement...and going fast in a straight line. That however doesn't make a better car.
Also, pure numbers of how many sold doesn't indicate one car manufacturer is better than another. Nobel makes cars that can and usually do beat Ferrari, however Nobel only makes and sells 50 cars every year and Ferrari makes and sells around 5,000 cars a year, excluding customer race cars.
You also have to remember, cars sold in the American market by both Japanese and American companies are nothing like what you can get in the rest of the world. They're specifically manufactured for the mind-frame of Americans, and that is mostly that they want big, heavy, fuel thirsty, pieces of sh*t cars. You find some of the American cars over in other markets like the Corvette and GT40's, but in tiny numbers and they're altered to meet emissions and other EU/JDM standards, but still suck down fuel like crazy.
Japanese cars in other markets are a hell of a lot different than what we get here. I'm lucky enough to have been inside Mazda's main development race team's facilities in the US and even the JDM spec Speed 6 and RX-8's are nothing like the ones sold in the American market. Parts may swap over, but the technology is different, especially since in almost every other country cars are speed capped/limited because there's no reason to have a 500+HP cars that can hit 200mph on the streets as a daily driver.
Edit again: I'm also a mechanic who's worked on both American and Japanese cars, and I'd rather work on a Japanese car any day of the week. I'm still very much fond of big V8's that can easily be made to produce 1000+HP, but they're still not necessarily better.