Why is it that better hospitals have less mortality and less complications when in fact everything depends on Hashgacha Pratit and prayers.

HaSham allows the world to work naturally, and also allows for the eficacy of prayer. We are unaware to what degree each works, but "olam k'minhago noheg", the world acts naturally, and therefor one should always strive to workwithin the natural order (get the best doctor, best treatment, etc) and believe that prayer will also help.