well first i would like to explain both ;
ayurveda : oldest form of medicine in the world, originated in and dates back to 3000 bc to 2000 bc.. ayurveda does not use any chemicals only herbs( so no side effects) and sometimes copper,gold,potassium permangante for increasing the immunity in humans( has limitation if it crosses that it leads to death). it uses simple instruments for surgeries and treatment. 2 great ancient doctors are sushrutha the surgeon(father of surgery) ad charaka the physician(father of medicine) were born on 8th century bc.they were the authors of charaka samhita and sushrutha samhita.
charaka samhita includes digestion,metabolism,immunity,genetics,a... of human body,etiology,physiology,embryology, e.t.c. he classified human body and character into three sections in his book charaka samhita.A physician who fails to enter the body of a patient with the lamp of knowledge and understanding can never treat diseases. He should first study all the factors, including environment, which influence a patient's disease, and then prescribe treatment. It is more important to prevent the occurrence of disease than to seek a cure -- charaka
sushrutha samhita describes 300 procedures of surgery and 120 surgical instruments. he made complicated surgeries like catarct,artificial limbs,plastic surgery,fractures,brain tumors,e.t.c. he was the first one in the world to use anesthesia and injection. ayurveda means science of longeivity and it could solve 90% of the modern surgeries through medicines.but it has a disadvantage that it reacts little slow but it can cure of the disease completely and make sure it does not occur again.but after the invention of injection by sushrutha reactions became fast.ayurveda is a master of nervous system,digestion,bones,anatomy,genetics,... e.t.c.
modern medicine : originated mostly i europe around 14th to 15th century ad. mostly everyone knew about this but still i would like to explain. it is not based on cure but postponing. it does not guarantee complete cure mostly based on surgeries but it can too solve all the diseases upto a limit it's advantage is treatment of cancer which is not described in ayurveda( only the basics are inscribed and it's prevention is detailedly explained). as it is based on chemicals side effects are common. it is based on modern bio tech machines. and is widely used in the world.great doctors are found in the world but mostly modern medicine seeks for the cure not for understanding the disease. for eg: if you go to the doctor with fever and tells 3 days he immediately judges it to be viral fever and prescribes some tablets,not knowing that fever is just an indicator malaria,dengu,typhoid,swine flu all start with fever only.so this a major drawback for modern medicine.
by the above comparison i prefer ayurveda better than modern medicine as it does has most of advantages of modern medicine and not postpones but cures. but if modern medicine combine with ayurveda we can make wonders.