That you don't define "better" makes your challenge meaningless.  If you go by public health statistics, there are about 20 nations that are generally considered to surpass us.  (Look it up.)  If you go by the citizen's feeling of confidence that he and his children will get needed care, regardless of his finances at the time, we aren't even in the competition--Canada and most of western Europe beat us easily.  If you go by the efficiency of payment system (for us, mostly private insurance), again we lose badly to both single-payer systems and regulated, subsidized insurance systems (like Germany).  I suppose you could say that, at least until recently, the U.S. has offered (but only to those who can afford it) more cutting-edge treatments than elsewhere.  (Such treatments are often wildly cost-ineffective--few lives saved versus astronomical costs.)  They're a poor way to rank a "health care system" supposed to serve over 300 million people